Cendrich. 


LIBRARY 

WIYERSITY  OF  CALIFORNIA 
RIVERSIDE 


TERS^OFMEDICIND 


OF 


^HOMINES  AD    DECS   NULLA  IN  ttE  r 

PRO  PI  us  ACCEDUNT   QUAM  •* 

SALUTEM  HOMINIBUS    DANDO. 

CICERO 


Masters  of  Medicine 

Title  Author 

JOHN  HUNTER  ....  Stephen  Paget 

WILLIAM  HARVEY   .         .         .  D* Arcy  Power 

SIR  JAMES  YOUNG  SIMPSON       .  H.  Laing  Gordon 

WILLIAM  STOKES      .         .         .  Sir  William  Stokes 

SIR  BENJAMIN  BRODIE     .         .  Timothy  Holmes 

CLAUDE  BERNARD    .         .         .  Sir  Michael  Foster 

HERMANN  L.  F.  VON  HELMHOLTZ  J.  G.  M-Kendrick 

In  Preparation 

THOMAS  SYDENHAM          .         .     y.  F.  Payne 
ANDREAS  VESALIUS  .         .         .     C.  Louis   Taylor 


M 


A5TER5 

OF 
EDICINE 


H.   L   F.   VON   HELMHOLTZ 


WASTERS     OF 
MEDICINE 


Hermann    Lud 
Ferdinand  von  Helmh 


JOHN    GRA  JRICK 


PROFESSOR  OF  PHYSIOLOGY  IN  THr 
AND  FfiLLO 

OF  EDINIll 


LOND 

,',-|7J3/l    HHOJ  YH    TKSJ  yjU'/^lM    HIAHOOTOH*!    A 
/.I    HSXAT 

'sTJOHMjaH   xov 

^1     .HT^1    Y-IU[    XIO 


FROM  A  PHOTOGRAPH  KINDLY  LENT  BY  LORD  KELVIN, 

TAKEN    IN 

PROFESSOR  VON  HELMHOLTZ'S  LABORATORY. 
ON  JULY  7TH,  1894 


Hermann   Ludwig 
Ferdinand  von  Helmholtz 


JOHN    GRAY    M'KENDRICK 
\\\ 

M.D.,  LL.D.,  F.R.SS.L.  AND   E. 

PROFESSOR  OF  PHYSIOLOGY  IN  THE  UNIVERSITY  OF  GLASGOW 

AND   FELLOW  OF  THE   ROYAL  COLLEGE  OF  PHYSICIANS 

OF  EDINBURGH 


L O ND O N 
T.    FISHER    UNWIN 

PATERNOSTER  SQUARE 


MDCCCXCIX 


Copyright  by   T.  Fisher  Unwin,  1899,  for  Great    Britain 

and  Longmans,   Green  &  Co.  for  the 

United  States  of  America 


TO    MY    FRIEND 

JAMES    DEWAR 

IN    MEMORY    OF    OLD    DAYS    OF 

MUTUAL    WORK    AND 

ENCOURAGEMENT 


PREFACE 


THIS  work  is  a  record  of  the  achievements  in 
scientific  discovery  and  invention  of  one  of 
the  greatest  minds  of  the  nineteenth  century. 
Helmholtz  was  one  whose  private  life  was 
known  only  to  a  few,  and  he  would  have 
instinctively  recoiled  from  biographical  revela- 
tions of  a  purely  personal  character.  At  the 
same  time,  I  have  endeavoured  to  give  the 
reader  some  idea  of  the  man  —  calm,  placid, 
reserved,  thoughtful  —  whose  love  of  truth, 
yearning  spirit  of  inquiry,  and  great  intel- 
lectual powers  give  him  a  place  in  the  front 
ranks  of  the  interpreters  of  Nature.  A  life 
full  of  intellectual  activity,  creative,  ever  pro- 
ductive, could  not  contain  much  in  the  way 
of  trivial  incident.  I  have  also  tried,  by 
following  a  historical  method,  to  trace  the 
history  of  any  branch  of  inquiry  up  to  the 


xiv  PREFACE 

point  when  it  came  under  the  survey  of 
Helmholtz,  and  then  I  have  given  an  account 
of  the  contributions  made  by  himself.  Few 
are  able  to  tread  in  the  footsteps  of  Helm- 
holtz, even  although  these  are  carefully  pointed 
out  by  a  competent  guide;  but  this  volume 
may  at  all  events  give  an  outline  of  the  paths 
along  which  he  trod. 

The  proofs  have  been  read  by  Mr  J.  L. 
Galbraith,  of  the  Library  of  the  University  of 
Glasgow,  to  whom  I  owe  my  thanks ;  and  I 
have  gratefully  to  acknowledge  much  valu- 
able assistance  and  friendly  criticism  from  Dr 
Cargill  G.  Knott,  Lecturer  on  Mathematical 
Physics  in  the  University  of  Edinburgh. 

The  characteristic  portrait  was  most  kindly 
lent  by  Lord  Kelvin.  It  was  taken  by  Mr 
Henderson,  a  student  of  physics  at  that  time, 
and  it  represents  Helmholtz  at  his  lecture  table 
on  July  7,  1894,  a  few  days  before  his  final 
illness: 

JOHN  G.  M'KENDRICK. 


UNIVERSITY  OF  GLASGOW, 
September,  1899. 


CONTENTS 


CHAP.  PAGB 

I.  CHILDHOOD  AND  EARLY  LIFE         .          .          I 
II.  STUDENT  LIFE  AND  EARLY  MANHOOD    .         8 

III.  SCIENCE  IN  GERMANY  IN  THE  EIGHTEENTH 

AND  EARLY  PART  OF  THE  NINETEENTH 
CENTURIES 18 

IV.  HELMHOLTZ  IN    BERLIN — FERMENTATION 

— ANIMAL  HEAT      .         .         .         .25 

V.  HELMHOLTZ  IN  BERLIN — THE  CONSERVA- 
TION OF  ENERGY       ....       39 

VI.  HELMHOLTZ  IN  KONIGSBERG — MEASURE- 
MENT OF  THE  RAPIDITY  OF  THE 
NERVOUS  IMPULSE  ....  58 

VII.  HELMHOLTZ  IN  KONIGSBERG — THE  OPH- 
THALMOSCOPE .         .          .         .         .71 

VIII.   HELMHOLTZ  IN  KONIGSBERG — THE   ME- 
CHANISM OF  ACCOMMODATION — FIRST 
VISIT  TO  ENGLAND   .         .         .         .88 
xv 


xvi  CONTENTS 

CHAP.  PAGE 

IX.  HELMHOLTZ    IN    KONIGSBERG —  ANIMAL 

ELECTRICITY 104 

X.  HELMHOLTZ  IN  KONIGSBERG — STUDIES  IN 

COLOUR 112 

XI.  HELMHOLTZ    IN   BONN  AND    HEIDELBERG 

— SENSATIONS  OF  TONE   .         .         .129 

XII.  HELMHOLTZ   IN   BONN  AND   HEIDELBERG 

— SENSATIONS  OF  TONE  CONTINUED.      145 

XIII.  HELMHOLTZ     IN     HEIDELBERG — MINOR 

PHYSIOLOGICAL  RESEARCHES       .          .169 

XIV.  HELMHOLTZ    IN    BERLIN — PHYSICAL    RE- 

SEARCHES   183 

XV.  HELMHOLTZ   IN    BERLIN — PHYSICAL   RE- 
SEARCHES CONTINUED        .         .         .201 

XVI.  HELMHOLTZ    IN   BERLIN — PHYSICAL    RE- 
SEARCHES CONTINUED        .         .         .233 

XVII.  THE  PHILOSOPHICAL  POSITION  OF  HELM- 
HOLTZ      250 

XVIII.  HELMHOLTZ  ON  ESTHETICS  .         .         .     268 
XIX.  HELMHOLTZ  AS  A  LECTURER  .         .     273 

XX.  HELMHOLTZ    IN   BERLIN — CLOSING   YEARS 

AND  PERSONAL  CHARACTERISTICS        .     279 

POEM — HERMANN  VON  HELMHOLTZ         .     289 

BIBLIOGRAPHY 291 

INDEX  .......     295 


Hermann  von  Helmholtz 

CHAPTER     I 

CHILDHOOD    AND    EARLY    LIFE 

TJERMANN  LUDWIG  FERDINAND 
-Fl  VON  HELMHOLTZ  was  born  on  August 
3 ist,  1821,  at  Potsdam,  near  Berlin.  He  was  the  son 
of  Ferdinand  Helmholtz,  a  teacher  of  philology  and 
philosophy  in  the  Gymnasium,  a  man  of  high  culture 
and  of  great  general  intelligence,  who  was  much 
respected  for  the  thorough  way  in  which  he  per- 
formed the  duties  of  his  position,  and  for  the  integrity 
of  his  character.  His  mother  was  the  daughter  of  a 
Hanoverian  artillery  officer  of  the  name  of  Penne, 
a  lineal  descendant  of  William  Penn,  the  great  Quaker 
who  founded  Pennsylvania  ;  while  the  grandmother,  on 
his  mother's  side,  sprang  from  a  family  of  French 
refugees,  of  the  name  of  Sauvage.  Thus  Helmholtz 
had  German,  English  and  French  blood  in  his  veins. 
We  are  free  to  speculate  as  to  the  origin  of  his  great 
A 


HERMANN  VON  HELMHOLTZ 

talents,  and  as  to  his  dignified  presence  in  mature  years. 
It  is  possible  that  something  of  his  calm,  reserved,  self- 
possessed  manner  may  have  come  through  the  maternal 
line  from  the  old  Quaker  statesman  who  made  his  mark 
on  the  new  world.  There  is  no  trace  of  any  hereditary 
aptitude  for  mathematics,  and  it  must  be  said  that  the 
atmosphere  of  his  father's  home  was  not  favourable 
to  the  development  of  any  latent  faculties  in  that 
direction. 

The  little  we  know  of  his  early  life  was  revealed 
by  Helmholtz  himself  in  a  speech  delivered  in  1891, 
in  reply  to  the  toast  of  his  health  at  a  banquet  given 
in  honour  of  his  seventieth  birthday.  For  the  first 
seven  years  of  his  life  he  was  a  weakly  boy,  confined 
for  long  periods  to  his  room,  and  frequently  to  his  bed  ; 
but  he  was  fond  of  such  amusements  as  were  possible, 
and  he  showed  great  activity  of  mind.  His  parents 
gave  him  much  of  their  time  and  attention.  Picture 
books  amused  him,  and  at  an  early  age  he  read  widely. 
A  collection  of  wooden  blocks  he  specially  mentioned 
as  a  favourite  plaything,  and  while  he  wiled  away  the 
time  with  these  blocks,  he  formed  from  them  some 
geometric  conceptions  that  were  the  first  indications 
of  mathematical  genius. 

By-and-by  he  was  able  to  go  to  school,  where  he 
passed  through  the  usual  routine  of  a  good  general 
education.  No  doubt  his  father's  influence  encour- 
aged him  to  the  study  of  languages,  of  literature,  and 
of  philosophy.  The  quality  of  his  mind,  however,  did 
2 


CHILDHOOD  AND  EARLY  LIFE 

not  fit  him  for  following  in  his  father's  footsteps. 
He  had  difficulty  in  acquiring  languages,  finding  it 
hard  to  remember  words,  idiomatic  expressions,  and 
irregular  grammatical  forms.  To  have  to  commit 
prose  to  memory  was  torture,  but  he  found  it  easy 
to  store  up  passages  of  poetry,  when  he  was  helped 
by  rhythm  and  rhyme.  His  father  observed  this 
peculiarity,  and  being  himself  an  enthusiastic  student 
of  poetical  literature,  he  introduced  his  boy  to  this 
golden  storehouse,  and  not  only  read  widely  with 
him,  but  encouraged  him  to  commit  to  memory  poems 
and  ballads  from  German  literature.  They  read 
Homer  together,  and  it  is  a  remarkable  indication  of 
the  breadth  of  his  early  education,  that  he  was  able  to 
read  the  fables  of  L^kman  in  the  original  Arabic  when 
he  was  twelve  years  of  age.  His  father  also  exercised 
him  in  the  composition  of  essays  and  even  of  verses, 
and  Helmholtz  remarks  that  although  the  verses 
showed  that  he  was  a  poor  poet,  the  practice  was 
invaluable  in  the  way  of  training  him  to  the  proper  use 
of  forms  of  expression.  No  doubt  the  home,  if  not 
scientific,  was  intellectual.  He  mentions  that  he  fre- 
quently listened  to  philosophical  discussions  between 
his  father  and  his  friends,  and  thus  he  early  became 
acquainted  with  some  of  the  problems  of  metaphysics, 
as  enunciated  by  Kant  and  Fichte. 

The  mind  of  Helmholtz  opened  up,  becoming  more 
receptive  and  retentive  when  the  world  of  nature  was 
placed  before   him,  and  when   he  was   introduced  to 
3 


HERMANN  VON  HELMHOLTZ 

phenomena.  Already  his  wooden  bricks  had  taught 
him  much  as  to  geometrical  relationships.  The  mind 
became  familiar  with  ideas  as  to  spacial  relations,  and 
as  to  the  adjustment  of  various  forms,  while  he  placed 
his  bricks  now  in  this  position,  now  in  that,  so  that 
when  he  began  the  systematic  study  of  geometry  at 
the  Normal  School  of  Potsdam  in  his  eighth  year, 
he  astonished  his  teachers  by  his  knowledge  of  many 
fundamental  truths.  He  was  already  beginning  to  try 
his  wings. 

As  he  became  stronger  in  body,  he  was  able  to 
ramble  with  his  father  in  the  beautiful  country  around 
Potsdam,  with  its  palaces  and  gardens,  and  he  began  to 
look  at  nature  with  his  own  eyes.  Not  only  was  the 
love  of  the  beautiful  in  nature  encouraged,  but  also  the 
sense  that  all  her  operations  were  ruled  by  law.  He 
was  now  attracted  to  physical  phenomena  more  than  to 
the  abstract  ideas  of  algebra  and  geometry,  and  he 
early  realised  that  a  knowledge  of  natural  events  and 
of  the  laws  that  regulate  them  was,  as  he  says,  the 
4  enchanted  key '  that  places  the  powers  of  nature  in 
the  hands  of  its  possessor.  Antiquated  text-books  of 
physical  science  found  on  the  bookshelves  of  his  father 
were  eagerly  read.  His  enthusiasm  also  found  vent  in 
attempts  at  experiment,  to  the  detriment,  he  said,  of 
his  mother's  furniture  and  linen.  He  constructed 
optical  apparatus  with  a  few  spectacle  glasses  and  a 
small  botanical  lens  belonging  to  his  father.  While 
the  class  in  the  Gymnasium  were  reading  Cicero 
4 


CHILDHOOD  AND  EARLY  LIFE 

or  Virgil,  most  of  which  was  tiresome  to  young 
Helmholtz,  he  was  endeavouring,  below  the  table,  to 
work  out  problems  and  draw  diagrams  relating  to  the 
passage  of  rays  of  light  through  a  telescope.  Even 
then  he  worked  out  for  himself  some  optical  principles, 
not  expounded  in  ordinary  text-books,  which  were  of 
use  to  him  in  later  years,  in  the  construction  of  the 
ophthalmoscope.  This  was  his  apprenticeship  in  the 
art  of  experimenting,  in  which  he  afterwards  became 
so  proficient  a  master.  He  learned  how  to  think  out 
the  conditions  of  an  experiment,  turning  the  question 
round  and  round,  so  that  he  might  view  it  on  all  sides, 
pondering  over  the  possible  ways  of  achieving  the  solu- 
tion of  the  mechanical  or  optical  problem  before  him, 
until  he  got  a  clear  idea  of  what  had  to  be  done.  He 
also  developed  a  passionate  zeal  to  find  out  the  realities 
of  things,  a  zeal  that  continued  throughout  life,  and 
appeared  to  grow  in  intensity  as  the  years  flew  onwards. 
He  was  never  satisfied  with  the  apparent  solution  of  a 
problem,  if  there  were  still  doubtful  points  in  it,  and 
these  he  invariably  attempted  to  clear  up  by  bringing 
them  fairly  before  his  own  mind. 

It  has  been  said  by  one  who  knew  him  well  at 
this  early  period  of  his  life,  that  he  was  faithful  to 
his  duties  in  great  as  well  as  in  small  matters.  He 
was  zealous  in  his  studies ;  and  in  the  autumn  of 
1838,  after  the  abiturienten  examination,  he  left  the 
Potsdam  Gymnasium  for  the  University  with  the 
following  certificate  from  his  Rector  : — 
5 


HERMANN  VON  HELMHOLTZ 

*  His  exceptionally  calm  and  reserved  disposition  is 
combined  with  great  intellectual  enthusiasm.  In  it 
we  recognise  an  excellent  combination  of  clear  and 
prudent  understanding  and  deep  good  nature.  His 
manners  bear  witness  to  a  carefully  preserved,  ex- 
ceptionally pure,  and  genuine  childlike  innocence. 
These  peculiarities,  along  with  the  richness  and 
power  of  his  mental  development,  give  an  agreeable 
and  captivating  impression,  and  justify  the  hope  that 
such  a  ground-soil  of  intellectual  life  will  only  bring 
forth  the  best  of  fruits.'  This  testamur  and  prophecy 
were  amply  justified  in  after  life. 

It  is  remarkable  that  his  mathematical  talents  were 
developed  without  the  aid  of  an  eminent  teacher. 
He  had  no  training  in  mathematics  such  as  has 
been  given  to  the  great  majority  of  physicists  who 
have  attained  eminence.  His  talent  was  not  fostered 
by  the  mathematical  atmosphere  of  a  great  university 
like  that  of  Cambridge,  nor  did  he  start  life  among 
his  comrades  with  the  blue  ribbon  of  a  high  wrangler- 
ship.  His  mathematical  development  was  silently 
carried  on,  so  that  some  of  his  early  friends,  such  as 
Briicke  and  Du  Bois  Reymond,  both  afterwards 
physiologists  of  the  first  rank,  who  were  his  fellow- 
students  at  the  Gymnasium,  were  not  aware,  even 
when  they  were  all  engaged  in  the  problems  of 
analytical  geometry,  how  transcendent  were  his 
latent  mathematical  powers. 

Such   was    his    early    training.      Throughout    life 
6 


CHILDHOOD  AND  EARLY  LIFE 

Helmholtz  manifested  the  same  mental  character- 
istics as  were  shown  in  his  early  years.  The  same 
love  of  nature,  the  same  desire  to  penetrate  her 
secrets,  the  same  determination  to  compel  nature  to 
explain  herself.  As  is  the  case  with  most  men  of 
genius,  he  awakened  early  to  his  vocation.  This 
awakening  of  a  young  spirit  may  come  in  many 
ways,  and  the  time  of  its  occurrence  is  always  of 
the  deepest  interest.  The  youthful  artist  then 
recognises  the  beautiful,  he  clothes  it  with  an  ideal 
which  is  the  product  of  his  own  mind,  and  to  give 
to  the  ideal  expression  in  form  and  colour  is  for  ever 
the  aim  of  his  life.  In  like  manner  the  young 
naturalist  opens  his  eyes  to  the  order  of  the  universe, 
he  is  impressed  by  the  majesty  of  law,  he  feels  the 
first  thrill  of  a  desire  to  understand  the  method  of 
nature's  working,  and  for  him,  in  all  his  future  life, 
the  driving  power  of  all  his  faculties  and  the  satis- 
faction of  all  his  ideals,  is  the  pursuit  of  truth. 


CHAPTER    II 

STUDENT    LIFE    AND    EARLY    MANHOOD 

IT  was  the  desire  of  Helmholtz  to  devote  his  life  to 
the  study  of  physics,  but  his  father,  who  had, 
out  of  his  limited  means,  to  maintain  a  family  of 
four  children,  showed  him  that  it  would  be  almost  im- 
possible to  earn  a  livelihood  by  cultivating  or  teaching 
pure  science,  and  he  wisely  counselled  his  son  to 
study  medicine  in  the  first  instance.  This  advice  was 
supported  by  the  practical  assistance  of  a  relative, 
Surgeon-General  Mursinna,  who  obtained  for  Helm- 
holtz admission  in  1838  as  a  bursar  into  the  Royal 
Medico-Chirurgical  Friedrich-Wilhelm  Institute  in 
Berlin,  an  academy  for  the  medical  education  of 
youths  of  promise,  given  freely  on  the  condition 
that  they  afterwards  become  surgeons  in  the  Prussian 
army.  The  students  of  this  institution  attended  the 
usual  courses  of  instruction  in  the  medical  department 
of  the  University,  and  were  afterwards  attached  for 
a  time  to  the  Charitd  Hospital.  Thus  Helmholtz 
was,  by  force  of  circumstances,  led  to  enter  the 
medical  profession,  and  in  due  time  he  obtained  his 
diploma  and  became  an  army  surgeon. 

In  after  life  Helmholtz  often  referred  to  the  great 
8 


STUDENT  LIFE  AND  EARLY  MANHOOD 

advantage  he  gained  by  being  obliged  to  pass  through 
the  curriculum  of  medical  study.  In  a  famous  lecture 
on  Thought  in  Medicine,  delivered  in  1877,  he  remarked, 
'  My  own  original  inclination  was  towards  physics ; 
external  circumstances  obliged  me  to  commence 
the  study  of  medicine.  It  had,  however,  been  the 
custom  of  a  former  time  to  combine  the  study  of 
medicine  with  that  of  the  natural  sciences,  and  what- 
ever in  this  was  compulsory  I  must  consider  fortunate  ; 
not  merely  that  I  entered  medicine  at  a  time  in 
which  any  one  who  was  even  moderately  at  home 
in  physical  considerations  found  a  virgin  field  for 
cultivation,  but  I  consider  the  study  of  medicine  to 
have  been  that  training  which  preached  more  im- 
pressively and  more  convincingly  than  any  other 
could  have  done,  the  everlasting  principles  of  all 
scientific  work  ;  principles  which  are  so  simple  and 
yet  are  ever  forgotten  again ;  so  clear  and  yet 
always  so  hidden  by  a  deceptive  veil.' l 

The  practical  side  of  the  medical  art  also  appealed 
to  his  kindly  nature.  In  the  same  lecture  he  remarks : 
1  Perhaps  only  he  can  appreciate  the  immense  im- 
portance and  the  frightful  practical  scope  of  the 
problems  of  medical  theory,  who  has  watched  the 
fading  eye  of  approaching  death,  and  witnessed  the 
distracted  grief  of  affection,  and  who  has  asked 
himself  the  solemn  questions,  Has  all  been  done 
which  could  be  done  to  ward  off  the  dread  event  ? 

1   Popular  Lectures,  1 88 1,  p.  2O2. 


HERMANN  VON  HELMHOLTZ 

Have   all    the    resources   and   all    the    means   which 
science  has  accumulated  become  exhausted  ? ' l 

About  this  time  there  was  a  distinguished  band  of 
youthful  students  at  the  University  of  Berlin,  who  all 
ultimately  became  men  of  scientific  eminence,  and 
who  made  their  mark  on  the  learning  of  the  follow- 
ing thirty  or  forty  years.  Here  Helmholtz  met  Du 
Bois  Reymond  (a  friend  of  his  school  days),  who 
afterwards  became  Professor  of  Physiology  in  the  Uni- 
versity of  Berlin,  and  who  systematised  and  developed 
the  department  of  electro-physiology  ;  Briicke,  who 
in  due  time  was  elected  to  the  Chair  of  Physiology  in 
Vienna ;  Virchow,  the  greatest  of  living  pathologists, 
who  still  holds  the  Chair  of  Pathology  in  Berlin,  while 
he  is  a  power  in  science  and  also  in  the  state  ;  and 
many  others.  These  all  clustered  round  the  feet  of 
the  greatest  physiologist  of  the  time,  Johannes  Miiller, 
who  taught  anatomy  and  physiology  in  the  university. 
It  so  happened  also  that  Gustav  Magnus  filled  the 
Chair  of  Physics.  These  two  distinguished  men 
represented  a  new  school  of  thought,  then  arising  in 
Germany,  that  which  rebelled  against  the  older 
metaphysical  school,  and  craved  for  the  investigation 
of  natural  phenomena.  They  attracted  many  dis- 
ciples, and  an  alliance  was  established  between  the 
physicists  and  chemists  on  the  one  hand,  and  the 
physiologists  on  the  other.  Thus  Gustav  Karsten, 
Heintz,  Knoblauch,  Clausius,  Kirchhoff,  Quincke, 

1  Popular  Lectures,  op.  cit.}  p.  203. 
IO 


STUDENT  LIFE  AND  EARLY  MANHOOD 

Werner  Siemens,  Tyndall  and  Wiedemann,  who  all 
became  remarkable  in  chemistry  or  physics,  joined 
Du  Bois  Reymond,  Helmholtz,  Briicke,  and  others, 
who  represented  the  physiological  school,  in  founding 
the  Physical  Society,  a  society  in  which  they  met  on 
equal  terms  and  freely  discussed  papers  dealing  with 
scientific  questions.1  It  is  impossible  not  to  notice 
the  great  preponderance  of  physicists  in  the  little 
band  ;  indeed  it  may  be  said  they  were  all  physicists, 
as  Du  Bois  Reymond  and  Helmholtz,  and  even 
Briicke,  approached  physiological  problems  from  the 
physical  side.  It  was  an  epoch  in  the  history  of 
science,  as  not  a  little  of  the  outcome  of  modern 
science,  and,  in  particular,  its  methods,  may  be 
traced  to  that  group  of  brilliant  young  men. 

There  can  be  little  doubt  that  Johannes  Miiller 
was  the  greatest  living  force  in  the  University  of 
Berlin  at  that  time.  A  man  of  indefatigable  industry 
and  perseverance,  with  an  energy  that  overflowed 
into  many  sciences,  a  man  of  worthy  aims  and  clear 
insight,  who  had  the  power  of  inspiring  the  youths 
who  hung  upon  his  words,  a  man  who  had  in  his 
great  text-book  collated  and  discussed  the  facts  of 


1  Du  Bois  Reymond  points  out  that  Carl  Ludwig  was  not  a  pupil  of 
Johannes  Miiller.  He  studied  at  Marburg  and  followed  his  own 
course,  ultimately  becoming  Professor  of  Physiology  in  Leipzig.  He 
became  a  physiologist  of  the  highest  eminence,  and,  both  by  his  own 
labours  and  that  of  his  numerous  pupils,  whom  he  attracted  from  all 
countries,  advanced  many  departments  of  physiological  science,  in  par- 
ticular our  knowledge  of  the  circulation  of  the  blood. 
II 


HERMANN  VON  HELMHOLTZ 

physiological  science  in  a  manner  that  in  some  re- 
spects resembled  the  great  work  of  Haller,  published 
a  century  before,  Johannes  Miiller  was  the  greatest 
biological  teacher  of  his  time.  In  some  ways  he 
resembles  John  Hunter  more  than  any  other  naturalist, 
but,  owing  to  the  circumstances  in  which  he  worked, 
he  left  behind  him  what  Hunter  did  not  leave — a  school 
of  ardent  disciples  imbued  with  the  spirit  of  the  master. 

Miiller  also  gave  a  great  impetus  to  the  movement 
that  had  already  begun  in  Germany  in  the  direction 
of  the  investigation  of  biological  problems  by  the 
methods  of  physical  and  chemical  science.  The 
principles  of  the  Baconian  philosophy  took  root  and 
influenced  science  much  later  in  Germany  than  in 
England ;  and  while  in  Germany  there  were,  up  to 
the  time  of  Miiller,  many  workers  who  were  in- 
fluenced by  that  school,  the  teaching  of  science,  and 
even  its  investigation,  more  especially  of  physiological 
science,  were  still  cramped  by  the  speculative  method 
of  metaphysics.  The  fundamental  problem  of  the 
nature  of  vital  action  was  held  generally  to  be 
beyond  the  domain  of  experimental  science ;  the 
doctrine  of  a  vital  force  which  modulated  and  held 
in  subjection  all  other  forces  held  sway ;  and  the 
great  conception  of  the  unity  of  origin  of  all  the 
tissues  of  the  body,  established  by  the  cell  theory  of 
Schleiden  and  Schwann,  had  not  yet  clearly  dawned 
on  the  minds  of  physiologists. 

The  influence  of  Miiller  was  felt  throughout  the 
12 


STUDENT  LIFE  AND  EARLY  MANHOOD 

world  after  the  publication  of  his  great  text-book  of 
physiology.  Here  were  found  not  only  all  the  facts 
of  the  science  then  known,  but  also  the  discussion 
of  principles.  In  particular,  the  physiology  of 
nerves,  of  nerve  centres,  and  of  the  senses,  was  ex- 
pounded in  a  manner  that  hitherto  had  not  been 
attempted.  Miiller  also  laid  the  foundations  of  the 
school  of  modern  experimental  psychology  by  placing 
on  a  clear  basis  the  mode  of  action  of  external 
stimuli  on  the  terminal  organs  of  sense.  He  showed 
that  in  whatever  way  a  terminal  organ  is  stimulated, 
the  result  is  the  same  in  consciousness,  according  to 
the  nature  of  the  particular  terminal  organ.  Thus 
if  we  stimulate  the  retina  of  the  eye  by  light,  or 
electricity,  or  heat,  or  mechanical  pressure,  as  by  a 
blow,  the  result  will  always  be  the  same — namely, 
the  sensation  of  a  flash  of  light,  possibly  of  colour. 
Further,  the  same  result  follows  any  kind  of  irritation 
of  the  optic  nerve,  which  conveys  the  impulses  from 
the  retina  to  the  brain  ;  and  from  this  he  deduced  the 
great  law  of  the  specific  sensibility  of  nerves,  by 
which  he  meant  that  each  nerve  of  special  sense  has, 
as  it  were,  its  own  sensibility,  so  that,  in  whatever 
way  it  may  be  stimulated,  the  result  will  always  be 
the  same.  This  doctrine  was  especially  fruitful  in 
the  hands  of  Helmholtz,  Fechner,  Brucke,  Hering, 
and  many  others.  It  was  a  great  step  to  recognise 
that  the  '  sensation  due  to  a  particular  nerve  may 
vary  in  intensity,  but  not  in  quality,  and  therefore 


HERMANN  VON  HELMHOLTZ 

the  analysis  of  the  infinitely  various  states  of  sensation 
of  which  we  are  conscious  must  consist  in  ascertain- 
ing the  number  and  nature  of  those  simple  sensations 
which,  by  entering  into  consciousness  each  in  its 
own  degree,  constitute  the  actual  state  of  feeling  at 
any  instant.' r  There  can  be  no  doubt  that  in  this 
and  many  other  departments  of  physiological  science, 
Miiller  awakened  new  ideas  and  stimulated  teachers 
of  youth.  Bowman,  Sharpey,  and  Carpenter,  in 
England ;  Allen  Thomson  and  John  Goodsir,  in 
Scotland  ;  Claude  Bernard  and  Vulpian,  in  France  ; 
Bonders,  in  Holland,  all  felt  his  influence.  Thus 
he  prepared  the  way,  not  only  for  the  labours  of 
Helmholtz,  and  the  other  young  men  who  were  his 
immediate  students,  but  for  the  remarkable  development 
of  physiological  science  that  has  taken  place  since  1840. 
Helmholtz  long  afterwards  wrote  words  that  apply 
with  striking  force  both  to  his  great  master  and  to  him- 
self. *  When  one  comes  into  contact  with  a  man  of  the 
first  rank,  his  spiritual  scale  is  changed  for  life.  Such 
a  contact  is  the  most  interesting  event  that  life  can  offer.' 
In  1842,  Helmholtz,  at  the  age  of  twenty-one,  pre- 
sented his  inaugural  thesis,  entitled  De  Fabrics 
systematis  nervosi  Evertebratorum^  in  which  he  made 
an  important  contribution  to  minute  anatomy.  In 
1833  Ehrenberg  discovered  in  ganglia,  which  are 
usually  small,  more  or  less  rounded  swellings  on 
nerves,  often  situated  at  the  apparent  junction  of 

1  Clerk  Maxwell  on  Helmholtz,  Nature,  vol.  v.,  p.  389. 

14 


STUDENT  LIFE  AND  EARLY  MANHOOD 

several  trunks,  peculiar  cells  or  corpuscles,  now 
called  nerve  cells  or  nerve  corpuscles.  These  cells 
are  found  also  in  all  nerve  centres,  such  as  the  spinal 
cord  and  brain,  and  they  lie  in  a  fine  variety  of  tissue, 
while  numerous  nerve  fibres  pass  through  the  ganglia, 
apparently  in  close  proximity  to  the  cells.  No  con- 
nection between  the  nerve  cells  and  the  nerve  fibres 
had  been  discovered,  although  Miiller  taught  that 
in  all  probability  such  a  connection  existed.  It  was/ 
reserved  to  Helmholtz  to  make  the  discovery.  With 
a  very  simple  and  primitive  form  of  a  compound 
microscope,  almost  as  different  from  the  splendid 
instruments  of  the  present  day  as  a  cheap  spyglass  is 
from  an  astronomical  telescope,  he  discovered  in  the 
ganglia  of  leeches  and  crabs  that  the  nerve  fibre 
originates  from  one  of  these  corpuscles.  This  was 
an  observation  of  fundamental  importance  as  showing 
the  connection  between  nerve  fibre  and  nerve  cell, 
and  it  has  been  extended  throughout  all  nerve  centres. 
The  so-called  axis  cylinder  of  a  nerve  fibre,  the 
central  part  of  a  nerve  fibre,  always  originates  from 
a  process  or  pole  or  prolongation  of  a  nerve  cell. 

Du  Bois  Reymond  mentions  that,  during  his  last 
year  of  medical  study,  Helmholtz  had  an  attack  of 
typhus  fever,   for  which  he  was  treated  gratuitously 
in  the  hospital,  while  his  small  weekly  allowance  for 
board    was    continued.       At    the    end    of    his    illness 
Helmholtz   found    himself    in    possession    of  a   little  : 
fund.     This   was  expended    in    the    purchase   of  the  ' 
15 


HERMANN  VON  HELMHOLTZ 

microscope  which  aided  him  in  the  research  for  his 
thesis.  The  incident  throws  light  on  the  economy 
and  simplicity  of  his  life  at  this  period. 

We  have  now  traced  Helmholtz  to  the  beginning 
of  his  career  as  a  contributor  to  science.  From  1842, 
when  his  first  paper  was  published,  and  when  he  was 
twenty-one  years  of  age,  on  to  1894,  the  year  of  his 
death,  when  he  had  reached  the  age  of  seventy-three, 
papers  flowed  from  his  pen  in  almost  uninterrupted 
succession.  With  the  exception  of  one  year,  1849, 
he  always  published  at  least  one  important  paper,  and 
usually  three  or  four,  and  occasionally  more,  each 
year,  so  that,  when  his  life's  work  was  over,  no  fewer 
-than  217  distinct  papers  and  books  represented  his 
labours.  Such  a  life  of  incessant  labour  could  not  be 
expected  to  be  full  of  incident.  It  is,  therefore, 
difficult  to  portray  his  life  step  by  step.  There  is 
not  much  to  lay  hold  of  in  following  his  career ; 
we  must  be  content  with  trying  humbly  to  tread 
in  his  footsteps  in  the  pathways  of  science,  and  to 
endeavour  to  grasp  the  scope  and  meaning  of  the 
many  discoveries  he  made.  The  great  variety  of 
his  work  in  so  many  sciences  suggests  the  method 
of  classifying  his  discoveries  and  then  attempting 
to  show  the  nature  of  his  investigations  in  physi- 
ology, in  physiological  optics,  in  acoustics,  in 
mathematics,  in  mechanics,  in  electrical  science. 
This  method,  while  it  would  give  coherence  to 
this  work,  would  make  a  biographical  sketch 
16 


STUDENT  LIFE  AND  EARLY  MANHOOD 

almost  impossible,  and  it  is  open  to  the  objection,  that 
it  would  render  each  chapter  a  somewhat  unsatis- 
factory resume  of  the  science,  without  making  us 
acquainted  with  the  man.  We  prefer,  therefore,  in 
the  following  chapters  to  trace  his  career,  as  far  as 
possible,  by  his  works,  as  these  were  given  to  the 
world  from  his  various  spheres  of  activity.  He  spent 
his  life  in  Berlin  from  1842  to  1847,  when  he  became, 
at  the  age  of  twenty-nine,  Professor  of  Physiology  in  ' 
Konigsberg ;  he  was  in  Konigsberg  from  1849  to 
1856,  when,  in  his  thirty-fifth  year,  he  was  removed 
to  the  Chair  of  Physiology  in  Bonn  ;  this  he  held 
till  1859,  when,  in  his  thirty-eighth  year,  he  became 
Professor  of  Physiology  in  Heidelberg  ;  here  he  re- 
mained till  1871,  when  he  was  called  to  occupy  the 
Chair  of  Physics  in  Berlin  in  his  fiftieth  year  ;  and 
this  position  he  held  until  his  death  in  1894.  It  will 
give,  we  think,  the  best  idea  of  the  man  to  endeavour 
to  cluster  his  discoveries  round  the  centres  where  they 
were  made.  Thus  we  will  see  how  his  mind  swung 
from  one  subject  to  another,  and  how  his  powers 
matured  until  he  became  a  giant  among  his  fellows. 
The  method  will  also  enable  us  to  appreciate  the 
value  of  his  contributions  to  science  with  reference 
to  the  time  and  circumstances  in  which  they  were 
made.  We  will  also  see  that  while  he  was  a  master"^ 
in  medicine  he  was  something  more,  and  that  at 
least  seven  sciences  will  hereafter  claim  Helmholtz 
as  one  of  their  most  distinguished  investigators. 


CHAPTER    III 

SCIENCE    IN     GERMANY    IN    THE    EIGHTEENTH    AND 
EARLY  PART   OF    THE    NINETEENTH    CENTURIES 

THE  adequate  recognition  of  the  work  of  a  great 
man,  in  any  sphere  of  intellectual  activity, 
depends  much  on  a  correct  appreciation  of  the  streams 
of  tendency  apparent  in  the  time  before  he  appeared. 
We  must  endeavour  to  discover  the  lines  along  which 
thought  was  progressing,  and  to  see,  not  from  our 
standpoint,  but  from  theirs,  the  questions  which  were 
then  agitating  the  minds  of  men.  This  will  enable 
us  to  estimate,  on  the  one  hand,  the  influence  of  the 
time  upon  the  man,  and  the  share  that  other  men's 
thoughts  had  in  moulding  his  character  and  directing 
his  mental  energies  ;  and,  on  the  other  hand,  the  extent 
to  which  he  reacted  on  the  conditions  surrounding 
him,  and  the  contributions  he  made  to  human  know- 
ledge. Men  of  science,  in  particular,  must  be  dealt 
with  in  this  way.  The  state  of  education,  especially  in 
the  universities,  the  facilities  for  scientific  work,  the 
current  of  scientific  opinion,  must  all  be  studied  before 
we  can  fairly  judge  as  to  what  the  man  was,  and  as  to 
what  work  he  accomplished.  One  result  from  such 
18 


SCIENCE  IN  GERMANY 

an  investigation  is,  that  we  see  that  the  great  thinker 
came  at  an  opportune  time.  There  are  times  in  the 
history  of  science  when  there  is  a  kind  of  quietism. 
Many  busy  workers  are  engaged  in  the  accumulation 
of  facts,  but  there  are  no  startling  discoveries  nor  broad 
generalisations  that  seem  to  put  things  in  a  new  light. 
Such  periods  are  unfavourable  to  the  production  of 
great  men.  Yet,  even  during  such  times,  there  may 
be  undercurrents  of  thought  making  for  great  ques- 
tions. Here  and  there  a  solitary  thinker  may  be 
brooding  over  great  problems,  and,  although  his 
thoughts  may  be  dark,  he  is  almost  unconsciously  pre- 
paring the  way  for  the  full  revelation  of  the  truth  to 
the  man  of  genius.  Thus  it  is  that  to  only  a  very 
few  is  vouchsafed  the  honour  of  making  an  entirely 
new  discovery.  This  is  an  occurrence  of  the  rarest 
kind.  The  rule  is  that  limited  observations  of  the 
truth  are  made  here  and  there  by  men  who  are  soon 
forgotten  (except  by  the  historian  of  science),  vague 
and  nebulous  speculations,  as  it  were,  float  in  the  air, 
and  at  last  an  epoch  arrives,  and  with  it  the  man. 
The  epoch  ushers  in  new  ideas,  new  modes  of  looking 
at  things,  new  generalisations  of  far-reaching  char- 
acter affect  the  views  of  scientific  thinkers,  and  with 
this  new  period  we  usually  associate  the  name  of  one 
man,  such  as  Copernicus,  Galileo,  Newton,  Linnaeus, 
Darwin.  Great,  individually,  as  such  men  were,  in 
estimating  their  work  we  must  remember  that  they 
were  not  only  highly  endowed,  but  that  they  were 


HERMANN  VON  HELMHOLTZ 

also  the  children  of  good  fortune.  They  came  on  the 
world's  stage  at  the  right  time,  they  caught  up  all  the 
impressions  of  the  science  of  their  day,  they  added  to 
this  the  product  of  their  own  labours,  and  thus  they 
gave  a  new  impetus  to  scientific  progress. 

The  career  of  Helmholtz  illustrates  what  has  been 
written.  To  understand  in  some  measure  how  he 
contributed  so  much  to  the  science  of  his  day,  we 
must  not  only  recognise  his  transcendent  genius,  but 
also  that  the  times  were  favourable  to  its  full  develop- 
ment. 

During  the  eighteenth  and  the  beginning  of  the 
nineteenth  century,  science  made  little  progress  in 
Germany. I  In  chemistry  the  phlogiston  theory  led 
men  in  the  wrong  direction  for  nearly  a  century.  The 
problems  of  physical  science  were  still  approached  by 
the  a  priori  method,  and  the  speculations  of  Schelling 
and  Hegel  were  not  favourable  to  any  method  that 
had  for  its  foundation  the  investigation  of  facts.  Here 
and  there  important  scientific  results  were  obtained, 
such  as  Chladni's  study  of  elastic  vibrations  of  plates, 
Ritter's  electrical  experiments,  and  Seebeck's  discovery 
of  thermo-electricity,  but  there  was  no  co-operation 
among  the  physicists,  and  there  was  no  common  goal 
towards  which  their  energies  were  directed. 

Physiology  had  not  yet  asserted  her  existence  as  a 
science  founded  on  observation  and  experiment.  She 

1  G.  Wiedemann,  Introduction  to  Helmholtz's  Wiuenschaftlicht 
Abhandlungtn.  Leipzig,  1895. 

20 


SCIENCE  IN  GERMANY 

was  still  the  handmaid  of  anatomy,  and  she  was  domin- 
ated by  the  metaphysical  idea  of  a  vital  force.  This 
idea  hindered  investigators  from  examining  many 
physiological  phenomena  which  are  under  the  same 
forces  as  those  at  work  in  the  inorganic  world,  and  the 
notion  that  vital  actions  were  dependent  on  molecular 
and  chemical  changes  in  living  tissues,  had  not  yet 
been  entertained. 

In  France,  however,  science  was  not  in  this  dormant 
state.  The  intellectual  unrest,  which  culminated  in 
the  Revolution,  led  to  almost  universal  scepticism,  a 
state  of  mind  which  found  expression  in  the  writings 
of  the  Encyclopaedists.  For  a  time  men  lost  faith  in 
the  methods  and  conclusions  of  philosophical  and 
ethical  systems,  and  thought  was  determined  towards 
physical  and  chemical  science.  Then  arose  Coulomb, 
Lavoisier,  Laplace,  Cuvier,  and  many  others,  and 
France  became  the  leader  in  scientific  investigation, 
more  especially  in  physics  and  chemistry.  This  state 
of  things  was  not  without  its  influence  on  Germany. 
Many  young  scientific  men  from  Germany,  such  as 
Alexander  von  Humboldt,  Mitscherlich,  and  Liebig 
received  their  training  in  Paris,  and  imbibed  the 
scientific  spirit  of  the  French  savants.  Such  men 
returned  to  their  own  country,  and  soon  occupied 
positions  of  influence  in  the  universities.  In  these 
days,  as  now,  Paris  was  to  a  large  extent  France,  and 
this  produced  a  concentration  of  scientific  effort  which 
did  not  take  place  till  a  later  period  in  Germany,  owing 


HERMANN  VON  HELMHOLTZ 

to  the  universities  of  the  latter  being  scattered  in  the 
various  states.  By  degrees,  however,  concentration 
also  occurred  in  Germany.  According  to  Wiedemann, 
an  important  school  of  mathematical  physics  arose  in 
Konigsberg,  and  at  last  in  Berlin,  as  in  Paris,  and 
largely  owing  to  the  influence  and  fame  of  Mitscher- 
lich,  a  scientific  centre  was  formed. 

The  earlier  workers  in  the  period  of  scientific 
awakening  were  such  men  as  Mitscherlich  and  Liebig 
among  chemists,  and  Ohm,  Franz  Neumann,  and 
Wilhelm  Weber  among  physicists.  These  were  soon 
joined  by  the  contingent  from  Berlin,  which  included 
PoggendorfF,  Riess,  Dove,  and  Magnus.  The  latter, 
Magnus,  became  especially  a  notable  teacher  and 
laboratory  worker,  influencing  both  by  teaching  and 
example  a  number  of  young  and  able  men.  These 
physicists  were  in  rebellion  against  the  metaphysical 
schools  which  had  so  long  dominated  the  thought  of 
Germany,  and  they  swung  almost  to  the  opposite 
extreme,  extolling  nothing  but  experience  and  experi- 
ment. For  a  time  the  collection  of  facts  seemed  to 
be  the  paramount  object  in  physical  research  ;  theory 
was  in  the  background.  So  far  did  Magnus  carry  this 
view,  that,  as  we  are  assured  by  Wiedemann,  he  was 
constantly  warning  his  pupils  not  to  plunge  too  deeply 
into  mathematics,  and  he  regarded  experimental  and 
mathematical  physics  as  two  separate  departments. 
In  this  way,  do  doubt,  the  Berlin  school  built  a  firm 
foundation  of  fact  for  theoretical  views,  as  distinguished 

22 


SCIENCE  IN  GERMANY 

from  notions  which  were  the  outcome  of  metaphysics  ; 
and  the  work  on  thermodynamics  of  Clausius,  one  of 
Magnus's  distinguished  pupils,  is  an  apt  illustration  of 
this  statement.     As  also  pointed  out  by  Wiedemann,\ 
the    writings   of  Helmholtz  and    Robert  Mayer  are  \ 
good    examples,   the    first  of  theory    developed    from 
experiment,  and  the  second  of  a  more  metaphysical 
mode  of  investigation. 

Empirical  physical  research  has  a  tendency  to  become 
one-sided,  and  after  it  has  been  indulged  in  for  a  time, 
it  is  almost  invariably  followed  by  a  more  general 
treatment  of  the  subject.  This  occurred  among  the 
disciples  of  Magnus.  Earnest  in  their  earlier  years  in 
the  discovery  of  facts,  in  their  latter  they  each  and  all 
were  engaged  in  the  contemplation  of  theoretical  views 
then  far  beyond  the  range  of  experimental  science. 

The  rise  of  the  physico-chemical  school  of  Berlin 
had  an  important  influence  on  the  development  of 
physiology  in  Germany.  Ernst  Heinrich  Weber  was 
no  doubt  the  first  to  ask  for  an  explanation  of  the 
phenomena  of  life  by  examination  of  these  phenomena 
by  physical  methods,  and  the  application  of  physical 
laws.  After  him  came  Johannes  Miiller,  who  was  at 
first  somewhat  wedded  to  the  older  quasi-metaphysical 
position,  but  in  his  later  years  he  also  took  up  the  views 
and  methods  of  Weber.  For  a  considerable  time,  how- 
ever, the  notion  of  a  vital  force  still  held  sway.  Pheno- 
mena in  living  things  were  supposed  to  be  different 
not  only  in  degree,  but  in  kind,  from  those  in  inorganic 
23 


HERMANN  VON  HELMHOLTZ 

matter.  If  this  notion  were  to  be  got  rid  of,  it  could 
only  be  by  prolonged  investigation  in  a  physico- 
chemical  direction.  Such  were  the  views  of  three 
young  physicists  and  physiologists,  Briicke,  Du  Bois 
Raymond  and  Helmholtz.  As  already  narrated, 
these  three  joined  the  physicists  and  chemists  in 
founding  the  Physical  Society  of  Berlin.  Here  they 
found  sympathy  and  encouragement.  Here  papers 
were  read  and  frankly  criticised.  Here  was  de- 
veloped, for  the  first  time,  an  attempt  to  investigate 
physiological  phenomena  by  the  methods  of  chemistry 
and  physics.  Physiology,  indeed,  was  regarded  as  in  a 
sense  a  branch  of  chemico-physics,  and  the  phenomena 
of  nature — chemical,  physical,  physiological — were  held 
to  be  controlled  by  one  general  principle,  or  rather  to 
depend  ultimately  on  the  properties  of  matter.  Some 
of  these  enthusiasts  took  even  a  wider  sweep,  and 
brought  into  their  net  the  phenomena  of  psycho- 
physics,  and  the  physical  and  physiological  foundations 
of  the  arts — sculpture,  painting  and  music. 

Helmholtz  was  without  doubt  the  most  distinguished 
of  this  group  of  young  men.  He  was,  to  use  Wiede- 
mann's  expression,  and  Wiedemann  was  a  contem- 
porary, head  and  shoulders  above  the  rest.  In  each 
department  of  scientific  labour  represented  by  the 
members  of  this  brilliant  galaxy,  he  acquired,  in  after 
life,  marked  distinction  ;  to  each  department  he  made 
vast  additions,  while  he  elevated  the  whole  body  of 
scientific  knowledge. 

24 


CHAPTER    IV 

HELMHOLTZ    IN    BERLIN — FERMENTATION — ANIMAL 
HEAT 

DURING  the  greater  part  of  the  period  from  his 
graduation  in  medicine  in  1842  till  his  appoint- 
ment to  the  Chair  of  Physiology  in  Konigsberg  in 
1849,  Helmholtz  resided  in  Berlin.  He  completed 
his  term  of  service  as  assistant  physician  in  the  La 
Charite  Hospital,  and,  in  1843,  he  returned  to  Pots- 
dam, where  he  discharged  the  duties  of  assistant  surgeon 
to  the  regiment  of  Red  Hussars.  Private  practice  he 
never  had  ;  all  his  time,  when  off  duty,  being  devoted 
to  science.  Coming  under  the  notice  of  Alexander  von 
Humboldt,  that  great  man  recognised  his  capacity, 
and  through  his  influence  he  was  relieved  from  mili- 
tary duties,  and  became  assistant  to  the  Anatomical 
Museum,  Lecturer  on  Anatomy  to  the  Academy  of 
Arts,  and  Extraordinary  Professor  of  Physiology  to 
the  Albert  University.  In  the  two  latter  appoint- 
ments it  is  interesting  to  know  that  he  succeeded  his 
friend  Ernst  Briicke,  who  subsequently  filled  with 
great  distinction  the  Chair  of  Rhysiology  in  Vienna. 
There  is  little  doubt  the  appointment  to  the  Academy 
25 


HERMANN  VON  HELMHOLTZ 

gave  his  mind  the  aesthetic  bias  so  apparent  in  after 
years.  His  researches,  however,  were  not  anatomical, 
but  physiological  and  physical. 

In  1843  h£  macle  an  important  contribution  to  the 
theory  of  fermentation.  This  process  has  long  been, 
and  indeed  still  is,  the  cause  of  much  controversy 
between  chemical  physicists  and  biologists,  and  from 
the  controversy  has  flowed  results  of  the  highest 
importance  to  humanity.  When  sugar  is  changed 
into  alcohol  and  carbonic  acid  in  the  ordinary  alcoholic 
fermentation,  the  process  is  in  some  way  related  to 
the  vegetable  cells  of  the  yeast  plant,  Saccharomycetes 
cerevisits,  first  seen  by  Leeuwenhoek  in  1680.  For 
many  years  these  minute  organisms  received  little  or 
no  attention,  but  in  1838  Schwann,  one  of  the 
founders  of  the  cell  theory,  and  Cagniard  de  la  Tour 
demonstrated  the  vegetable  nature  of  these  yeast  cells, 
and  showed  that  they  grew  and  multiplied  in  saccharine 
solutions.  For  the  first  time  it  was  asserted  that 
fementation  in  some  way  depended  on  the  action  of 
living  things.  Previous  to  1838  Berzelius  suggested 
that  the  action  of  the  yeast  is  what  is  called  catalytic, 
that  is  causing  a  separation  or  decomposition  of  the 
atoms  forming  the  sugar  in  a  way  similar  to  the 
action  of  platinum  black  on  peroxide  of  hydrogen, 
when  the  latter  gives  up  an  atom  of  hydrogen. 
Liebig  strongly  contended  that  there  is  no  necessary 
connection  between  the  fermentive  process  and  the 
development  of  living  organisms,  and  he  held  that  the 
26 


HELMHOLTZ  IN  BERLIN 

organisms  may  simply  produce  a  substance,  the  mole- 
cular vibrations  of  which  may  cause  a  re-arrangement 
of  the  atoms  of  the  substance  undergoing  fermenta- 
tion. According  to  this  view  fermentation  is  essenti- 
ally a  chemical  process.  A  substance  of  unstable 
chemical  composition  is  formed  by  the  yeast  cells, 
and  by  vibrations,  due  to  chemical  changes  in  this 
substance,  movements  are  communicated  to  the  atoms 
of  sugar,  so  that  these  are  re-arranged  to  form  alcohol, 
carbonic  acid,  and  small  quantities  of  a  few  other 
bodies.  The  growth  of  the  yeast  cell  is  only  in- 
directly connected  with  fermentation. 

For  a  considerable  time  this  theory  held  its  ground, 
owing  largely  to  the  prestige  of  its  illustrious  author ; 
but  facts  came  to  light  that  again  concentrated  the 
attention  on  the  biological  aspect  of  fermentation. 
Thus  Gay-Lussac  showed  that  clean  grapes  or  boiled 
grape  juice  passed  into  the  Torricellian  vacuum  of 
a  barometer  tube  kept  free  from  fermentation  for  any 
length  of  time,  but  that  if  a  single  bubble  of  air 
were  admitted  fermentation  soon  appeared.  About 
1838  Schwann  repeated  Gay-Lussac's  experiment,  and 
showed  that  if  the  air  were  admitted  to  the  vacuum 
through  a  red  hot  tube  then  fermentation  did  not 
occur.  Clearly  it  was  something  in  the  air  that 
caused  fermentation,  and  that  something  was  destroyed 
by  heat.  Further,  it  was  shown  that  active  fermentation 
was  always  accompanied  by  increased  growth  of  the 
yeast,  and  that  conditions  of  temperature  affected  the 
27 


HERMANN  VON  HELMHOLTZ 

process.  Thus  a  temperature  of  from  20°  C.  to  24° 
C.  was  most  favourable  to  it,  while  the  process  was 
arrested  at  60°  C.  Boiling  destroyed  fermentation. 
It  was  also  arrested  by  freezing,  but  on  careful  thaw- 
ing the  process  was  resumed.  Schwann  also  estab- 
lished the  identity  of  the  processes  of  fermentation 
and  putrefaction  by  showing  that  they  both  were 
connected  with  the  development  of  living  organisms, 
and  he  laid  the  foundation  for  the  splendid  researches 
of  Pasteur,  which  have  created  the  modern  science  of 
bacteriology. 

The  contribution  made  to  this  discussion  by  Helm- 
holtz  in  1843  is  of  no  mean  importance.  He  showed, 
first,  that  the  oxygen  produced  by  electrolysis  in  a 
sealed-up  tube  containing  boiled  fermentable  fluid, 
did  not  cause  fermentation.  He  also  performed  the 
following  ingenious  experiment :  he  placed  a  bladder 
full  of  boiled  grape  juice  in  a  vat  of  fermenting  juice, 
and  found  that  the  fluid  in  the  bladder  did  not  ferment. 
Thus  the  cause  of  the  fermentation  could  not  pass 
through  the  wall  of  the  bladder.  If  the  fermentation 
were  excited,  as  held  by  Liebig,  by  a  substance  formed 
by  the  yeast  cells,  and  presumably  soluble,  one  would 
have  expected  it  to  pass  through  the  wall  of  the 
bladder  ;  but  if  the  process  were  caused  by  the  small 
yeast  cells,  then  one  can  see  why  fermentation  was 
not  excited,  as  the  yeast  cells  could  not  pass  through 
the  membrane.  Soon  afterwards  Mitscherlich  showed 
that  the  yeast  cells  could  not  pass  through  a  septum 
28 


HELMHOLTZ  IN  BERLIN 

of  filter  paper ;  Hoffmann  proved  that  a  layer  of  cotton 
wool  had  the  same  effect  ;  and  Schroeder  and  Dusch 
made  the  important  demonstration,  that' air  filtered 
through  cotton  wool  is  incapable  of  exciting  putre- 
faction in  a  putrescible  fluid  that  has  been  boiled. 
The  cotton  wool  has  sifted  from  the  air  the  bodies 
that  cause  putrefaction,  just  as  the  wall  of  the  bladder, 
the  septum  of  filter  paper,  or  the  layer  of  cotton  wool, 
prevents  the  passage  of  the  yeast  cells  from  a  fermenting 
to  a  fermentable  fluid.  The  conclusion,  then,  is  irresist- 
ible that  the  living  organisms  in  the  air  and  in  the  yeast 
are  the  cause  of  putrefaction  and  fermentation.  It  will 
thus  be  seen  that  the  comparatively  simple  observa- 
tions of  Helmholtz  were  of  fundamental  importance. 

Surrounded  as  he  was  by  young  physicists,  it  is 
not  surprising  that  Helmholtz  approached  physiology 
on  its  physical  side.  Physiology  is  essentially  a  com- 
posite science,  inasmuch  as  it  is  closely  related  to 
anatomy,  physics  and  chemistry.  In  the  solution  of 
physiological  questions,  the  physiologist  must  collect 
facts  from  these  three  departments  of  knowledge. 
Thus,  for  example,  in  investigating  the  phenomena  of 
the  circulation  of  the  blood,  the  physiologist,  in  the 
first  place,  must  be  acquainted  with  the  structure  of 
the  heart  and  blood  vessels,  with  the  position  and 
appearances  of  the  valves  in  the  heart  and  in  many  of 
the  veins,  and  with  the  nature  of  the  minute  texture 
or  tissue  of  the  heart,  as  revealed  by  the  microscope. 
Then  he  considers  the  circulation  as  a  problem  of 
29 


HERMANN  VON  HELMHOLTZ 

hydrodynamics,  investigating  and  measuring  the  force 
and  frequency  of  the  heart's  contractions,  and  deter- 
mining the  causes  of  the  high  pressure  maintained  in 
the  arterial  system,  the  nature  of  the  pulse,  and  the 
uniform  flow  of  the  blood  in  the  capillaries.  These 
investigations  are  all  of  a  physical  character.  Finally, 
if  the  physiologist  pursues  his  analysis  still  farther, 
he  may  examine  the  chemical  characteristics  of  the 
tissues  forming  the  heart  and  vessels,  the  nature  of 
chemical  compounds,  both  organic  and  inorganic, 
existing  in  these  tissues,  and  the  influence  of  chemical 
substances  upon  the  living  heart.  Almost  every 
physiological  problem  may  be  attacked  in  a  similar 
way,  and  it  can  only  be  fully  solved  when  all  the 
information  derived  from  anatomy,  chemistry  and 
physics  is  brought  to  bear  upon  it.  It  will  also  be 
evident  that  some  physiologists  are  attracted  to  one 
aspect  of  the  subject,  while  others  are  drawn  to 
another.  One  man  endeavours  to  explore  the  mystery 
of  living  action  by  the  microscopical  examination  of 
tissues,  living  and  dead  ;  another  works  at  the  chemical 
constitution  of  organs  and  tissues,  and  tries  to  get  a 
glimpse  into  the  nature  of  the  chemical  processes 
associated  with  life  ;  while  a  third  investigates  the 
phenomena  as  special  problems  in  physics.  Helmholtz 
was  an  outstanding  representative  of  the  latter  class, 
and  he  was  so  largely  by  reason  of  his  special  aptitude 
for  physical  and  mathematical  research,  and  of  his 
surroundings.  He  might  properly  be  described,  even 
30 


HELMHOLTZ  IN  BERLIN 

at  this  early  stage  of  his  career,  as  a  highly-trained 
physicist  interested  in  physiological  pursuits. 

It  is  interesting  to  observe,  that  while  physiology  is 
largely  indebted  to  physics,  the  latter  science  owes  not 
a  little  to  physiology,  inasmuch  as  the  consideration  of 
physiological  phenomena  has,  on  several  notable  occa- 
sions, led  the  physicist  into  a  new  and  fruitful  line  of  re- 
search. The  beginning  of  modern  electrical  science 
will  for  ever  be  traced  back  to  the  well-known  observa- 
tions of  Galvani  on  the  twitching  of  frogs'  legs  near 
an  electrical  machine,  to  his  speculations  on  the  exist- 
ence of  an  animal  electricity,  and  to  the  celebrated 
controversy  that  arose  between  Galvani  and  Volta,  a 
controversy  in  which  many  of  the  most  learned 
physicists  and  physiologists  of  the  day  took  part.  In 
like  manner,  the  discussion  of  questions  as  to  the 
nature  of  animal  heat  contributed  not  a  little  to  the 
doctrine  of  the  conservation  of  energy.  Helmholtz 
took  a  foremost  part  in  this  movement,  and  there 
can  be  no  doubt  he  was  led  into  it,  in  the  first 
instance,  by  physiological  considerations. 

The  physical  properties  of  dead  matter  are,  as  a 
rule,  more  easily  observed  and  registered  than  the 
physiological  properties  of  living  matter,  and  they  lend 
themselves  more  readily  to  mathematical  investigation. 
Hence  physical  science  is  much  farther  advanced  than 
physiological  science.  The  physicist  is  surer  of  his 
ground.  The  physiologist  has  to  deal  with  the 
mysterious  condition  we  call  vitality.  It  is  therefore 
31 


HERMANN  VON  HELMHOLTZ 

not  astonishing  that  physicists,  as  a  rule,  are  shy  of 
dealing  with  physiological  problems,  and  that  they 
regard  many  of  them  as  practically  insoluble.  In  the 
judgment  of  the  physicist,  life,  vitality,  the  mysteri- 
ous something  apparently  unknowable,  so  interferes 
with  and  obscures  the  play  of  the  ordinary  physical 
forces,  as  to  lead  him  to  doubt  whether  the  physical 
phenomena  of  living  matter  can  ever  be  thoroughly 
understood.  Now  it  is  remarkable  that,  although 
Helmholtz  was  already  at  the  age  of  twenty-five  a 
great  physicist,  he  boldly  entered  on  physiological 
research  with  the  assured  conviction  that  the  play  of 
the  physical  forces  in  living  matter  was  under  the 
same  laws  as  in  dead  matter,  and  that  the  only  way  to 
investigate,  with  success,  the  phenomena  of  living 
matter,  was  to  examine  them  by  physical  methods,  and 
to  submit  them,  as  far  as  possible,  to  physical  analysis. 
It  was  in  this  spirit  that  he  began  to  investigate  the 
phenomena  of  animal  heat,  and  this  investigation  led 
him  to  lay  the  foundations  of  the  great  doctrine  of  the 
conservation  of  energy.  The  subject  occupied  much 
of  his  attention  from  1844  to  1848,  and  he  returned 
to  it  in  1850,  1852,  1855  and  1859.  The  old  view 
that  heat  was  a  variety  of  imponderable  matter  had 
been  attacked  long  before  by  Voltaire,  who,  in  a  series 
of  elaborate  experiments,  endeavoured  to  prove  that  it 
was  only  a  kind  of  internal  movement ;  and  in  1798 
Count  Rumford,  one  of  the  founders  of  the  Royal 
Institution,  after  executing  a  series  of  experiments  on 
32 


HELMHOLTZ  IN  BERLIN 

the  production  of  heat  by  friction,  established,  in  a 
comparatively  rough  way,  the  dynamical  theory  of 
heat,  in  which  heat  is  regarded  as  an  accident  or  con- 
dition of  matter,  a  phenomenon  produced  by  c  a  motion 
of  its  ultimate  particles.' 

Helmholtz  studied  the  exchanges  of  matter  that 
occur  in  connection  with  muscular  contractions,  and 
he  made  the  important  observation,  that  such  ex- 
changes are  always  accompanied  by  the  disengagement 
of  heat.  This  indicated  that  animal  heat,  as  produced 
by  a  muscle,  arises  from  the  chemical  phenomena 
occurring  in  the  muscle.  Before  this  research,  Mat- 
teucci  had  apparently  shown  the  production  of  heat 
during  muscular  contraction  by  passing  thermo-electric 
needles  into  the  muscles  of  a  living  warm-blooded 
animal,  and  connecting  the  needles  with  a  thermal 
galvanometer  ;  but  as  in  his  experiments  the  blood  was 
flowing  through  the  muscle,  the  proof  that  the  in- 
crease of  temperature  observed  during  the  muscular 
contraction  was  due  to  changes  in  the  muscle  itself  was 
not  complete.  Helmholtz  got  rid  of  the  difficulty  of 
having  to  deal  with  an  organ  through  which  streams  of 
blood,  possibly  of  different  temperatures,  were  flowing, 
by  making  observations  on  the  isolated  muscles  of 
c  the  old  martyr  of  science,'  the  frog.  He  devised  a 
triple  thermo-electric  junction  of  iron  and  German 
silver,  so  made  that  it  could  be  passed  through  the 
muscles  of  the  thigh  of  a  frog.  A  similar  set  of 
junctions  were  kept  at  a  temperature  as  uniform  as 
c 


HERMANN  VON  HELMHOLTZ 

possible,  outside  the  muscles  of  the  frog,  and  the  two 
sets  of  junctions  were  connected  with  a  thermal 
galvanometer,  so  sensitive,  that  deflections  equivalent 
in  thermal  value  to  the  y^Vu^h  of  a  degree  Centigrade 
could  be  detected.  When  the  muscles  were  caused  to 
contract,  by  electrically  stimulating  the  sciatic  nerve, 
the  junctions  in  the  muscle  became  warmer  than 
those  outside  the  muscle,  as  indicated  by  a  deflection 
of  the  needle  of  the  galvanometer,  and  as  the  galvano- 
meter had  been  empirically  graduated,  the  actual  rise 
of  temperature  was  at  once  estimated.  It  was  thus 
shown  that  a  single  muscular  contraction  would  give  an 
increase  of  from  '001°  C.  to '005°  C.,  and  that  tetanus, 
or  cramp,  lasting  for  two  to  three  minutes,  would 
cause  a  rise  of  from  '014°  C.  to  *oi8°  C.  He  failed, 
however,  to  detect  heat  in  active  nerves.  These 
quantities  of  heat  are  no  doubt  small,  but  their  detec- 
tion showed  that  the  molecular  processes  occurring 
in  the  contracting  muscle  actually  produce  heat. 

Helmholtz  also  extended  his  observations  to  the 
general  phenomena  of  animal  heat.  On  Lavoisier's 
assumption  that  the  amount  of  heat  liberated  could 
be  determined  by  the  quantities  of  oxygen  consumed 
and  of  carbonic  acid  produced,  it  had  hitherto  been 
found  that  there  was  a  discrepancy  between  the 
amount  of  heat  actually  given  off  by  the  body  of  an 
animal  in  a  given  time  and  the  amount  to  be  expected 
from  calculation.  The  calculated  amount  of  heat 
was  usually  more  than  that  given  off  the  living  body. 
34 


HELMHOLTZ  IN  BERLIN 

Helmholtz  showed  that  less  heat  might  be  given  off 
than  could  be  estimated  from  the  complete  oxidation 
of  the  food  supplied,  indicating  that  the  oxidation 
processes  in  the  body  were  incomplete.  He  also 
computed  the  amount  of  heat  given  off  by  various 
channels  as  2'6  per  cent,  in  heating  excrementitious 
matters,  2'6  per  cent,  in  warming  the  air  of  expira- 
tion, 1 4' 7  per  cent,  by  evaporation  of  the  lungs,  and 
8o*i  per  cent,  by  evaporation  of  sweat  and  radiation 
and  conduction  by  the  skin.  These  results  have  been 
corroborated  and  extended  by  many  subsequent  ob- 
servers, and  it  has  been  conclusively  established  that 
the  heat  of  the  combustion  of  the  food,  as  determined 
by  a  calorimeter,  is  equal  to  the  heat  given  off  by  an 
animal ;  in  short,  that  an  animal  is  a  living  calorimeter 
in  which  the  food  stuffs  are  oxidised  or  burnt. 

A  new  investigation  almost  invariably  demands  the 
use  of  new  appliances.  New  ideas,  new  conceptions 
of  method,  spring  up  in  the  mind  of  the  experimenter, 
and  a  call  is  at  once  made  on  his  powers  of  invention. 
This  is  felt  even  in  a  well-furnished  laboratory,  and  of 
course  much  more  when  the  investigator  enters  on 
what  is  a  virgin  field  of  research.  Helmholtz,  when 
he  began  the  investigation  of  muscular  contraction, 
had  to  invent  many  of  his  tools.  About  this  period 
his  friend,  Du  Bois  Reymond,  was  laying  the  founda- 
tions of  his  life-long  work  on  electro-physiology,  and 
he  also  invented  many  appliances.  There  is  little 
doubt  Helmholtz  and  he  assisted  each  other  in  de- 
35 


HERMANN  VON  HELMHOLTZ 

vising  apparatus  by  which  the  phenomena  of  muscular 
contraction  could  be  accurately  studied.  Employing 
the  method  of  causing  a  contracting  muscle  to  write 
its  curve  on  the  blackened  surface  of  a  revolving 
cylinder,  or  on  a  moving  glass  plate,  a  method  of 
observing  the  time  relations  of  motor  phenomena 
first  suggested  by  Thomas  Young,  Helmholtz  de- 
vised the  well-known  myograph,  or  muscle  writer. 
Schwann  had  already  worked  with  a  rude  instrument, 
in  which  the  contracting  muscle  was  caused  to  pull  on 
a  lever  near  its  fulcrum,  and  no  doubt  he  was  the  first 
to  obtain  a  muscle  curve,  but  Helmholtz  improved  the 
instrument  by  making  the  lever  light,  and  at  the  same 
time  rigid,  and  by  other  mechanical  contrivances. 
Further,  he  endeavoured  to  keep  the  living  muscle  in 
conditions  as  favourable  as  possible  by  covering  the 
part  of  the  apparatus  containing  the  muscle  with 
a  glass  case,  under  which  pieces  of  blotting  paper, 
moistened  with  water,  were  placed.  This  '  moist 
chamber,'  as  it  is  technically  called,  became  a  space 
saturated  with  aqueous  vapour,  and  thus  the  muscle 
and  nerve  were  kept  in  fairly  natural  conditions,  and 
the  effects  of  cooling  and  drying  were  obviated. 

Helmholtz  also,  in  connection  with  this  research, 
made  arrangements  by  which  the  nerve  or  muscle 
could  be  stimulated  by  electric  shocks  of  short  dura- 
tion and  of  a  known  intensity.  He  applied  to  the 
well-known  induction  coil  of  Du  Bois  Reymond, 
designed  for  physiological  purposes,' a  modification  of 
36 


HELMHOLTZ  IN  BERLIN 

Neef's  interrupter,  by  which  the  circuit  in  the 
primary  coil  was  opened  and  closed,  and  as  the  inter- 
rupter works  automatically,  a  rapid  series  of  shocks 
may  be  transmitted  to  the  nerve  or  muscle.  It  was 
soon  found  that,  with  this  arrangement,  the  opening 
shock  acts  more  powerfully  on  the  muscle  than  the 
closing  shock,  in  other  words,  the  opening  shock  has 
the  greater  intensity.  This  arises  from  the  develop- 
ment, at  the  moment  of  closing  the  primary  current, 
of  an  extra  current  in  the  primary  coil,  which,  being 
in  the  reverse  direction  to  that  of  the  main  primary 
current,  so  retards  the  development  of  the  latter  as  to 
prolong  the  time  during  which  the  secondary  current 
flows,  and  thus  make  it  pass  through  a  lower  maxi- 
mum intensity  than  is  reached  by  the  secondary 
current  at  opening  when  the  change  of  the  primary  is 
more  abrupt,  and  the  secondary  current  lasts  for  a 
correspondingly  shorter  time.  The  total  quantity  of 
current  coming  from  the  secondary  coil  is  the  same 
whether  the  primary  circuit  is  being  opened  or 
closed  ;  but  the  secondary  current,  excited  at  opening, 
attains  momentarily  a  greater  intensity.  Hence  the 
opening  shock  is  the  more  stimulating.  As  in  stimu- 
lating a  nerve  or  muscle  by  an  induction  coil  it  is 
important  to  stimulate  with  rapid  opening  and  closing 
shocks  of  the  same  intensity^  Helmholtz  so  modified 
the  Neef's  interrupter  as  to  equalise  the  currents. 
By  his  arrangement  the  current  in  the  primary  circuit 
is  not  wholly  cut  off.  It  is  merely  short-circuited. 
37 


HERMANN  VON  HELMHOLTZ 

Thus  the  primary  circuit  is  always  closed  ;  but  the 
decrease  of  current  at  the  instant  of  short-circuiting 
has  the  same  kind  of  effect  in  producing  a  secondary 
current  as  when  the  primary  circuit  is  completely 
opened.  But  because  the  primary  circuit  remains  a 
closed  circuit,  the  extra  current  of  self-induction 
retards  the  rate  at  which  the  current  decreases,  just  as 
the  extra  current  retards  the  development  of  the 
current  at  closing.  Thus,  the  conditions  under 
which  the  secondary  currents  at  closing  and  at 
opening  are  produced  are  fairly  similar  ;  the  intervals 
of  time  during  which  they  last  are  approximately 
equal ;  and  the  maximum  intensities  reached  by  them 
are  almost  exactly  the  same.  In  this  way  the  opening 
shock  becomes  nearly  equal  to  the  shock  from  the 
secondary  coil  at  the  moment  of  closing.1  This 
clever  device  is  a  good  illustration  of  the  ingenuity 
of  Helmholtz  and  of  his  grasp  of  the  technique  of 
electrical  experimentation. 

1  For  details,  see  M'Kendrick's  Text-Book  of  Physiology,  vol.  i.,  p.  374. 
Glasgow,  1888. 


CHAPTER    V 

HELMHOLTZ    IN    BERLIN— THE    CONSERVATION    OF 
ENERGY 

THE  researches  on  muscular  motion  and  on  heat 
led  Helmholtz  to  the  study  of  the  great 
question  of  the  relation  to  each  other  of  the  forces 
of  nature,  and  especially,  and  in  the  first  instance, 
to  the  relation  of  these  forces  to  the  phenomena  of 
life.  What  is  life  ?  was  a  problem  often  before  his 
mind.  Was  the  living  state  to  be  explained  by  the 
interplay  of  the  same  chemical  and  physical  forces 
as  were  at  work  in  the  outer  world  ?  Or,  was  Stahl's 
view  to  be  accepted,  that  while  the  forces  were  the 
same  in  living  as  in  dead  matter,  they  were  all 
subject  to  a  living  power  or  principle  which  held 
them  together  and  caused  them  to  work  in  a  particular 
way  till  death  came,  when  the  physical  and  chemical 
forces,  now  liberated  from  control,  assumed  their 
supremacy  and  the  matter  forming  the  body  again 
returned  to  the  inorganic  world  ?  Was  the  energy 
of  life  continually  replenished  from  some  external 
source  ;  or  was  it  dependent  on  the  energy  of  the 
39 


HERMANN  VON  HELMHOLTZ 

forces  of  nature  supplied  to  it  from  the  outer  world  ? 
Was  the  living  body,  in  short,  only  a  minute  portion 
of  the  mechanism  of  the  cosmos  ;  or  was  there  some- 
thing beyond,  some  spiritual  fuel  continually  being 
added  to  its  vital  fires  ?  Helmholtz  thought  that  if 
the  life  was  fed  from  some  such  source  of  external 
energy,  then  the  living  body  was  an  example  of  a 
perpetuum  mobile,  a  perpetual  motion,  an  idea  he  had 
often  heard  ridiculed  in  the  philosophical  discussions 
that  were  not  infrequent  in  his  father's  home. 

If,  again,  the  natural  forces  were  found  competent 
to  explain  the  phenomena  of  life  without  the  assump- 
tion of  a  vital  force,  how  were  these  forces  related  to 
each  other  ?  About  this  period  Helmholtz  filled  the 
humble  office  of  assistant  in  the  library  of  the  Friedrich 
Wilhelm  Institute,  and  in  what  he  modestly  terms 
his  '  idle  moments,'  he  had  read  the  works  of  Euler, 
Daniel  Bernoulli,  d'Alembert,  and  other  mathe- 
maticians of  the  eighteenth  century,  no  mean  in- 
dication of  his  mathematical  powers,  and  he  thus 
became  equipped  for  the  discussion  of  the  great 
question.  He  was  especially  acquainted  with  the 
manifold  applications  made  by  Daniel  Bernoulli,  of 
Leibnitz's  idea  of  vis  viva. 

Such  considerations  led  Helmholtz,  in  his  twenty- 
sixth  year,  to  write  his  famous  essay,  Ueber  die  Erhaltung 
der  Kraft — on  the  Conservation  of  Force — one  of  the 
epoch-making  scientific  papers  of  the  century.  Clerk 
Maxwell  has  well  said  : — '  To  appreciate  the  full 
40 


HELMHOLTZ  IN  BERLIN 

scientific  value  of  Helmholtz's  little  essay  on  the 
Conservation  of  Force,  we  should  have  to  ask  those 
to  whom  we  owe  the  greatest  discoveries  in  thermo- 
dynamics and  other  branches  of  modern  physics,  how 
many  times  they  have  read  it  over,  and  how  often 
during  their  researches  they  felt  the  weighty  state- 
ments of  Helmholtz  acting  on  their  minds  like  an 
irresistible  driving  power  ? '  I 

The  essay  was  read  to  the  Physical  Society  of 
Berlin  on  the  23rd  of  July  1847,  an(^  ^  created  much 
excitement  in  the  distinguished  band  of  youthful 
workers.  The  author  showed  himself,  at  one  stroke, 
to  be  a  mathematician  of  the  first  order,  but  he  also 
enunciated  as  a  fundamental  principle  of  physics  the 
conservation  of  force,  just  as  Lavoisier,  seventy  years 
before,  had  made  that  of  the  persistence  of  matter  the 
fundamental  principle  of  chemistry.  He  showed  that 
'  if  the  forces  acting  between  material  bodies  were  equi- 
valent to  attractions  or  repulsions  between  the  particles 
of  these  bodies,  the  intensity  of  which  depends  only  on 
the  distance,  then  the  configuration  and  motion  of 
any  material  system  would  be  subject  to  a  certain 
equation,  which,  when  expressed  in  words,  is  the 
principle  of  the  conservation  of  energy.' 2  In  less 
technical  language,  he  established  mathematically  that 
'force'  (Kraft),  or,  as  it  is  now  termed,  energy,  is 
indestructible,  and  he  shows  that  this  principle  'con- 
tradicts no  known  parts  of  science,  while  it  is  con- 

1  Nature,  op.  cit.         2  Clerk  Maxwell,  Nature,  of,  clt. 
41 


HERMANN  VON  HELMHOLTZ 

firmed  in  a  striking  manner  in  a  great  number  of 
instances.'  Hence  it  follows  that  the  total  quantity 
of  energy  or  capacity  for  work  in  the  universe  is 
constant,  and  remains  eternal  and  unchanged  through- 
out all  the  vicissitudes  of  matter.  Energy  can  change 
its  form  and  locality  without  its  quantity  being 
changed.  The  universe  possesses  a  store  of  energy 
which  is  not  altered  by  any  change  of  phenomena, 
and  the  quantity  can  neither  be  increased  nor 
diminished.  Fifteen  years  afterwards,  in  1862, 
Helmholtz,  in  a  lecture,  thus  states  the  principle  : — 
c  If  a  certain  quantity  of  mechanical  work  is  lost,  we 
obtain  an  equivalent  quantity  of  heat  or  of  chemical 
force,  and,  conversely,  when  heat  is  lost  we  gain  an 
equivalent  quantity  of  chemical  or  mechanical  force  ; 
and,  again,  when  chemical  force  disappears,  an 
equivalent  of  heat  or  work ;  so  that,  in  all  these 
interchanges  between  various  inorganic  natural  forces, 
working  force  may  indeed  disappear  in  one  form, 
but  then  it  reappears  in  exactly  equivalent  quantity 
in  some  other  form  ;  it  is  thus  neither  increased  nor 
diminished,  but  always  remains  in  exactly  the  same 
quantity.  .  .  .  The  same  law  holds  good  also  for 
processes  in  organic  nature,  so  far  as  the  facts  have 
been  tested.' J  [For  the  word  *  force '  it  would  be 
better  to  use  the  term  c  energy.'] 

Such    a    conception    of   the    material    world    met 
with    much    opposition.      The    older    physicists   of 

1   Helmholtz's  Popular  Scientific  Lectures,  1873,  p.  360. 
42 


HELMHOLTZ  IN  BERLIN 

Berlin — Dove  and  Riess  —  would  not  admit  the 
principle  ;  Magnus  modestly  declined  to  express  an 
opinion,  as  he  thought  there  should  be  a  distinction 
between  mathematical  and  experimental  physics ;  the 
mathematicians  shook  their  heads,  and  we  have  it 
on  the  authority  of  Du  Bois  Reymond  that  only 
Jacobi,  who  himself  had  done  excellent  work  in 
mechanics,  saw  its  truth.  Helmholtz,  referring  in 
after  years  to  this  opposition,  said  he  was  met  by 
some  of  the  older  men  by  such  a  remark  as  this, — 
'  This  has  already  been  well  known  to  us ; 
what  does  this  young  medical  man  imagine  when 
he  thinks  it  necessary  to  explain  so  minutely  all  this 
to  us  ? '  PoggendorfF  actually  refused  to  insert  the 
memoir  in  his  famous  periodical  Annalen^  on  the 
ground  of  its  theoretical  character.  Du  Bois 
Reymond  took  the  manuscript  to  the  publisher, 
George  Ernest  Reimer,  then  engaged  in  bringing 
out  Du  Bois's  famous  papers  on  animal  electricity,  and 
he  not  only  published  the  paper,  but  gave  Helmholtz 
a  honorarium,  a  pecuniary  recognition  seldom  awarded 
to  an  abstruse  scientific  work.  The  value  of  the 
work  was  soon  recognised  by  the  military  authorities  ; 
Helmholtz  became  a  marked  man  ;  and  with  the 
characteristic  aptitude  of  the  Germans  for  putting 
the  right  man  in  the  right  place,  he  was  relieved 
largely  from  military  duties,  and  encouraged  to  go 
on  with  purely  scientific  work.  KirchhofF,  Clausius, 
Du  Bois  Reymond,  and  others  of  the  young  and 
43 


HERMANN  VON  HELMHOLTZ 

brilliant  school,  were  enthusiastic  in  their  approbation. 
Du  Bois  Reymond  remarks,  with  some  humour, — 
'  His  supporters  declared  that  he  had  set  in  motion 
the  conservation  of  another  force,  much  more  in- 
teresting for  us,  the  mind  of  Helmholtz  himself.' 1 

It  is  now  a  matter  of  common  knowledge,  that 
while  the  principle  of  the  conservation  of  energy 
slowly  unfolded  itself  to  the  minds  of  the  great 
scientific  thinkers  of  the  earlier  part  of  this  century, 
the  root  of  the  idea  must  be  traced  back  to  the  in- 
tellectual giants  Newton,  Descartes  and  Leibnitz. 
Professor  Tait  has  shown  that  Newton  undoubtedly  2 
was  in  possession  of  the  principal  facts  of  the  con- 
servation and  transformation  of  energy.  In  the 
expression  of  his  third  law  of  motion,  *  to  every  action 
there  is  always  an  equal  and  contrary  reaction,'  the  words 
'action'  and  '  reaction'  are  interpreted  by  Newton  him- 
self in  two  senses.  Between  any  two  bodies  connected 
together,  such  as  a  weight  resting  on  a  table,  there  is 
always  an  equal  and  opposite  reaction.  The  weight 
presses  on  the  table  and  the  table  presses  on  the 
weight.  Two  bodies  may  also  be  connected  by  some 
invisible  link,  such  as  exists  between  bodies  that  are 
affected  by  magnetic  attraction,  and  yet  the  law 
holds  good.  But  action  and  reaction  may  occur  in 
another  sense.  'If  the  activity  of  an  agent  be 

1  Du  Bois  Reymond's  GedHchtnissrede.     Berlin,  1896. 

2  Tail's  Lectures  on  Recent  Advances  in  Physical  Science,  1885.     Lect. 
ii.,  p.  27.     London,  1885. 

44 


HELMHOLTZ  IN  BERLIN 

measured  by  the  product  of  its  force  into  its  velocity, 
and  if  similarly  the  counter  activity  of  the  resistance 
be  measured  by  the  velocities  of  its  several  parts 
multiplied  into  their  several  forces,  whether  these 
arise  from  friction,  cohesion,  weight  or  acceleration, 
activity  and  counter  activity  in  all  combinations  of 
machines  will  be  equal  and  opposite.'  In  overcoming 
resistance,  as  when  work  is  spent  in  altering  the 
shape  of  a  body,  work  is  done  against  the  elastic 
forces  of  the  body  worked  against,  and,  according  to 
Newton's  statement,  the  amount  of  work  spent,  or 
the  rate  of  spending  work  in  distorting  the  body,  is 
equal  to  the  amount  of  work  done  or  the  rate  of 
doing  work  against  the  elastic  forces.  The  work  is 
stored  up  in  the  distorted  body  as  potential  energy. 
Suppose,  again,  work  is  expended  in  a  body  where 
there  is  no  resistance  from  friction,  cohesion  or 
weight,  it  will  be  spent  in  overcoming  the  inertia  of 
a  body  and  increasing  its  velocity,  that  is  to  say,  the 
kinetic  energy  of  the  body  increases.  In  such  a  case 
the  'rate  at  which  work  is  spent  is  measured  by  the 
product  of  the  momentum  into  the  acceleration  in  the 
direction  of  the  motion.'  We  know  that  when 
work  is  done  against  friction,  an  amount  of  heat  is 
produced  exactly  proportional  to  the  amount  of  work 
expended.  In  Newton's  day,  this  had  not  been 
experimentally  proved ;  otherwise  Newton  would 
probably  have  definitely  formulated  the  law  of  the 
conservation  of  energy.  As  Professor  Tait  says — 
45 


HERMANN  VON  HELMHOLTZ 

'  What  Newton  really  wanted  then  was  to  know 
what  becomes  of  work  that  is  spent  in  friction.' 

Descartes  affirmed  the  doctrine  of  the  constancy  of 
the  quantity  of  motion,  that  is  of  momentum,  in  the 
world.  Leibnitz,  in  whose  dynamical  views  of  nature 
force  was  the  ultimate  reality,  contended  that  Des- 
cartes's  statement,  that  motion  is  measured  by  velocity, 
should  be  abandoned  for  the  conception  of  a  vis 
matrix^  a  moving  force  measured  by  the  square  of  the 
velocity.  He  enunciated  in  1686  the  principle  of 
the  conservation  of  vis  viva^  and  came  near  a  full 
mathematical  expression  of  the  law  of  the  conserva- 
tion of  energy.  Both  Descartes  and  Leibnitz  were 
correct  in  their  contentions,  and  the  principle  of 
Descartes  may  be  called  the  conservation  of  momen- 
tum, while  that  of  Leibnitz  is  a  partial  statement 
of  the  conservation  of  energy.1 

The  discussion  is  closely  connected  with  the  views 
held  by  thinkers  regarding  the  nature  of  heat.  Thus 
Bacon  wrote :  <  Heat  is  a  motion,  expansive,  re- 
strained, and  acting  in  its  strife  upon  the  smaller 
particles  of  matter.' 2 

John  Locke,  by  a  priori  reasoning,  had  also  made  a 
happy  guess,  that  heat  was  not  matter  but  motion, 
that  it  'was  a  brisk  agitation  of  the  particles  of 
matter,'  but  the  statement  was  unsupported  by 
experimental  evidence. 

1  Sorley,  Art.  Leibnitz  in  Encycl.  Britann.,  vol.  xiv.,  p.  422. 

2  Bacon,  Speddin^i  Translation,  vol.  iv. 

46 


HELMHOLTZ  IN  BERLIN 

About  1798  Count  Rumford  performed  his  famous 
experiments  on  the  boring  of  cannon,  and  he  observed 
that  the  heat  produced  was  much  greater  than  that 
of  boiling  water.  The  older  theorists  held  that  heat 
was  a  substance,  but  Rumford 's  work  went  far  to 
prove  that  it  was  not  matter.  The  proof  was 
conclusively  given  by  Humphry  Davy,  who  ob- 
tained sufficient  heat  to  melt  ice  by  rubbing 
two  pieces  of  ice  together.  In  1812  Davy  wrote: 
{ The  immediate  cause  of  the  phenomena  of  heat, 
then,  is  motion,  and  the  laws  of  its  communication 
are  precisely  the  same  as  the  laws  of  the  communi- 
cation of  motion.'  Professor  Tait  remarks  in  this 
connection  :  *  If  Davy  had  with  this  statement 
taken  into  account  the  second  interpretation  of 
Newton's  third  law,  the  dynamical  theory  of  heat 
would  have  been  his.' 

It  is  said  that  Montgolfier  entertained  the  idea  of 
the  equivalence  of  heat  and  mechanical  work,  and  his 
nephew  Seguin  performed  experiments  with  a  steam 
engine,  in  which  he  endeavoured  to  ascertain  whether 
the  same  quantity  of  heat  reached  the  condenser  as 
had  left  the  boiler.  Had  he  succeeded  in  showing 
that  less  heat  reaches  the  condenser  than  had  left 
the  boiler,  he  would  have  found  that  the  heat 
apparently  lost  was  in  proportion  to  the  mechanical 
work  performed  by  the  engine. 

The  notion  of  the  correlation  of  the  physical  forces 
was  slowly  shaping  itself.  Mrs  Somerville's  book  on 
47 


HERMANN  VON  HELMHOLTZ 

the  Connection  of  the  Physical  Sciences  was  published 
in  1834,  but  little  is  said  about  the  'connections,' 
except  that  a  knowledge  of  one  science  is  often 
essential  to  the  successful  prosecution  of  another. 
In  January  1842,  Grove  delivered  a  lecture  in  the 
London  Institution  on  the  Correlation  of  the  Physical 
Forces,  which  was  afterwards  expanded  into  a  well- 
known  volume.  This  work  shows  that  of  the 
various  forms  of  energy  existing  in  nature,  any  one 
may  be  transformed  into  any  other,  the  one  form 
appearing  as  the  other  disappears.  No  doubt  this 
book,  written  in  a  clear  and  lambent  style,  familiarised 
the  public  mind  with  the  new  conception,  and  it 
also  influenced  scientific  opinion.  Clerk  Maxwell 
says  of  this  epoch  in  the  history  of  science  :  *  The 
fathers  of  dynamical  science  found  a  number  of 
words  in  common  use  expressive  of  action  and  the 
results  of  action,  such  as  force,  power,  action,  impulse, 
impetus,  stress,  strain,  work,  energy.  They  also  had 
in  their  minds  a  number  of  ideas  to  be  expressed,  and 
they  appropriated  these  words  as  they  best  could  to 
express  the  ideas.  The  words  force,  vis,  kraft,  came 
most  readily  to  hand.' 

In  and  about  1842  the  speculations  and  researches 
of  Robert  Mayer  of  Heilbronn  appeared.  Only  to  a 
limited  degree  an  experimenter,  Mayer  had  yet 
wonderful  clearness  of  vision  and  originality,  and 
although  his  premises  were  sometimes  inadmissible, 
and  his  reasoning  faulty,  he  enunciated  a  true 
48 


HELMHOLTZ  IN  BERLIN 

theory  and  developed  its  applications,  more  especially 
in  the  organic  world.  He  gave  a  popular  exposition 
of  the  theory  of  the  transformation  of  energy  into 
heat,  and  he  even  calculated  the  dynamical  equivalent 
of  heat,1  giving  it  as  365  kilogramme-meters,  instead 
of  the  true  equivalent,  ascertained  experimentally  by 
Joule  to  be  425  kilogramme-meters,  for  i°C.  (equivalent 
to  772  foot-pounds  for  i°  F.).  His  papers  produced 
little  effect,  even  in  Germany,  at  the  time  of  their 
publication,  partly  because  they  were  founded  so  little 
on  experimental  enquiry,  and  partly  because  they 
were  the  work  of  an  obscure  physician  in  a  country 
town.  His  writings  had  no  influence  on  science 
until  long  after  the  truth  had  been  proclaimed  by 
Helmholtz.  The  science  of  energy  would  have 
progressed  much  as  it  has  done  had  Mayer  never 
lived  ;  but,  on  the  other  hand,  had  the  doctrine  of 
the  conservation  of  energy  come  first  from  Mayer, 
there  would  still  have  been  the  need  of  a  mathe- 
matical thinker  like  Helmholtz  to  establish  it  as  a 
law  of  nature.  It  is  only  fair  to  mention  Mayer's 
obscure  position  (no  fault  of  his)  as  an  explanation 
of  the  fact  that,  when  Helmholtz  wrote  his  essay, 
he  was  totally  unacquainted  with  Mayer's  work. 
When,  in  subsequent  years,  it  was  brought  under 
his  notice,  no  one  was  more  generous  than 
Helmholtz  in  his  estimation  of  the  merits  of  his 

1  Mayer,  Liebig's  Annalen,  vol.  xlii.,  p.  233  ;  Phil.  Mag.,  4th  series, 
vol.  xxiv.,  p.  371  ;  Resume'm  Phil.  Mag.,  xxv.,  p.  378. 
D 


HERMANN  VON  HELMHOLTZ 

compatriot ;  and  the  question  of  priority,  which  was 
for  a  time  keenly  discussed  by  the  friends  of 
both  parties,  was  one  that  gave  no  concern  to 
his  great  mind.  It  is  said  that  he  bestowed  even 
more  credit  on  Mayer  than  the  latter  claimed  for 
himself. 

The  theory  of  the  conservation  of  energy  was 
established  experimentally  by  Colding  of  Copenhagen 
and  Joule  of  Manchester.  The  works  of  Sadi  Carnot 
(1824)  and  Clapeyron  (^1833)  in  France  in  relation 
to  heat  were  also  of  first-rate  importance.  Carnot 
had  shown  that  work  was  done  where  heat  was 
transmitted  from  a  body  of  a  higher  temperature  to 
a  body  of  lower  temperature.  The  Danish  philo- 
sopher was  less  of  an  experimenter  than  Joule,  but 
he  expresses  his  conclusions  in  the  following  unmis- 
takable language  : — 

'  Force  is  imperishable  and  immortal ;  and,  therefore, 
where  and  wherever  force  seems  to  vanish  in  perform- 
ing certain  mechanical,  chemical  or  other  work,  the 
force  then  merely  undergoes  a  transformation  and  re- 
appears in  a  new  form,  but  of  the  orginal  amount,  as  an 
active  force.1  In  the  year  1843  this  idea,  which  com- 
pletely constitutes  the  new  principle  of  the  perpetuity 
of  energy,  was  distinctly  given  to  me,  the  idea  itself 
having  been  clear  to  my  own  mind  nearly  four 
years  before,  when  it  arose  at  once  in  my  mind  by 

1  Colding'i  Treatise,  1843,  Royal  Society  of  Copenhagen.     Theses  con- 
cerning Force.     Nogle,  Saetn'mger  am  Krtefterne. 
50 


HELMHOLTZ  IN  BERLIN 

studying  d'Alembert's  celebrated  and  successful 
enunciation  of  the  principle  of  active  and  lost 
forces  ;  but,  of  course,  the  new  principle  was  not  as 
clear  to  me  from  the  beginning  as  it  was  when  I 
wrote  my  treatise  in  1843.  I  closed  my  discussion 
by  showing  that  the  discovery  of  a  perpetuum  mobile 
would  be  possible  if  my  principle  was  wrong.' x  Here 
he  anticipates  Helmholtz. 

The  researches  of  Joule  were  final  and  conclusive. 
Extending  over  a  period  of  several  years,  probably 
originating  before  1840  (the  first  paper  appeared  in 
that  year),  they  are  models  of  skilful  experiment  and 
accurate  induction.  They  were  concluded  in  1849, 
when  the  dynamical  equivalence  of  heat  was  finally 
established.  This  led  to  the  enunciation  of  the  first 
law  of  thermo-dynamics,  that  c  when  equal  quantities 
of  mechanical  effect  are  produced  by  any  means  what- 
ever from  purely  thermal  sources,  or  lost  in  purely 
thermal  effects,  then  equal  quantities  of  heat  are  put 
out  of  existence  or  are  generated ;  and  for  every  unit 
of  heat  measured  by  the  raising  of  a  pound  of  water, 
i°  Fahrenheit  in  temperature,  you  have  to  expend 
772  foot-pounds  of  work.'  The  principle  was  estab- 
lished by  Joule  for  mechanical  work,  current  electricity, 
electro  -  magnetism  and  light.  Thus  the  grandest 
generalisation  of  physical  science — the  conservation  of 
energy — is  founded  on  the  mechanical  theory  of  heat.2 

1  Colding,  Phil.  Mag.,  Jan.  1864. 

2  Tait,  Recent  Advances,  op.  cit.,  p.  64. 

51 


HERMANN  VON  HELMHOLTZ 

The  first  in  Great  Britain  to  recognise  the  immense 
importance  of  the  principle  was  William  Thomson, 
now  Lord  Kelvin,  who  applied  it  with  such  force  to 
thermo-dynamics  as  to  practically  create  this  depart- 
ment of  science.  He  also  formulated  the  comple- 
mentary doctrine  of  the  dissipation  of  energy. 

It  has  been  necessary  to  give  this  slight  sketch  of 
the  development  of  these  great  ideas  so  as  to  enable 
one  to  estimate  with  some  degree  of  accuracy  how 
much  was  contributed  by  Helmholtz.  He  approached 
the  subject  from  the  purely  mathematical  point  of 
view.  With  the  writings  of  Newton,  Leibnitz, 
Descartes  and  d'Alembert  in  the  field  of  his  mental 
vision,  he  starts  by  making  two  assumptions.  The 
first  is  as  follows : — Suppose  matter  to  '  consist  of 
ultimate  particles  which  exert  on  each  other  forces 
whose  directions  are  those  of  the  lines  joining  each 
pair  of  particles,  and  whose  amounts  depend  simply  on 
the  distance  between  the  particles  ;  suppose,  in  fact, 
that  something  akin  to  gravitation  force  exists  amongst 
all  the  particles  of  matter  in  the  universe,  that  each 
particle  attracts  every  other  particle  with  a  force 
which  depends  only  on  the  distance  between  them, 
not  in  any  way  upon  the  sides  which  are  turned  to 
one  another,  so  that  if  you  know  the  distance  between 
them  you  know  the  amount  of  the  attraction,  and  that 
the  attraction  shall  also  be  (in  accordance  with 
Newton's  Third  Law  of  Motion)  in  the  direction 
of  the  line  joining  them.  If  that  assumption  is  made, 
52 


HELMHOLTZ  IN  BERLIN 

then  it  is  a  consequence  of  the  laws  of  motion  of 
gross  matter  that  if  all  the  forms  of  energy  depend 
upon  motion  or  position  of  particles,  the  conservation 
of  energy  must  hold,  and  also  that  the  so-called 
perpetual  motion  would  be  impossible  under  any 
circumstances.' 

As  an  alternative,  Helmholtz  reasoned  in  the 
following  manner  : — Assume  the  impossibility  of  the 
so-called  perpetual  motion,  and  consider  also  Newton's 
second  interpretation  or  explanation  of  the  Third 
Law  of  Motion,  then  these  two  thoughts  would 
by  themselves  lead  to  the  proof  of  the  principle  of 
the  conservation  of  energy.  But  the  perpetual 
motion  has  been  demonstrated  by  experiment  to  be 
impossible.  This  being  an  experimental  fact,  and 
Newton's  statement  being  also  universally  true,  the 
principle  of  the  conservation  of  energy  is  established. 
Thus  Helmholtz,  by  a  purely  theoretical  considera- 
tion of  the  matter,  made  the  great  discovery  for 
himself.  It  is  no  detraction  to  the  work  of  Helm- 
holtz on  this  subject  that  it  was  theoretical.  One 
of  the  main  objects  of  theoretical  research  is  to  find 
the  point  of  view  in  which  the  subject  appears  in 
its  greatest  simplicity.  It  is  also  its  purpose  to  give 
the  form  in  which  the  results  of  experiments  may 
be  expressed.  Theory  leads  to  the  conception  of 
functions  the  forms  of  which  must  be  settled  by 
experiment. 

As  already  mentioned,  the  application  of  the  prin- 
53 


HERMANN  VON  HELMHOLTZ 

ciple  of  the  conservation  of  energy  to  living  beings 
was  first  clearly  made  by  Robert  Mayer.  Nothing 
will  give  a  better  notion  of  this  line  of  thought  than 
the  following  quotation  from  Mayer's  well-known 
paper  on  4  Organic  Motion  and  Nutrition': — 

1  The  second  question  refers  to  the  cause  of  the 
chemical  tension  produced  in  the  plant.  This  ten- 
sion is  a  physical  force.  It  is  equivalent  to  the  heat 
obtained  from  the  combustion  of  the  plant.  Does 
this  force,  then,  come  from  the  vital  processes,  and 
without  the  expenditure  of  some  other  form  of  force  ? 
The  creation  of  a  physical  force,  of  itself  hardly 
thinkable,  seems  all  the  more  paradoxical  when  we 
consider  that  it  is  only  by  the  help  of  the  sun's  rays 
that  plants  perform  their  work.  By  the  assumption 
of  such  a  hypothetical  action  of  the  "vital  force," 
all  further  investigation  is  cut  off,  and  the  application 
of  the  methods  of  exact  science  to  the  phenomena 
of  vitality  is  rendered  impossible.  Those  who  hold 
a  notion  so  opposed  to  the  spirit  of  science  would 
be  thereby  carried  into  the  chaos  of  unbridled  phan- 
tasy. I  therefore  hope  that  I  may  reckon  on  the 
reader's  assent  when  I  state,  as  an  axiomatic  truth, 
that  during  vital  processes  a  conversion  only  of  matter^ 
as  well  as  of  force,  occurs^  and  that  creation  of  either  the 
one  or  the  other  never  takes  place. 

'The  physical  force  collected  by  plants  becomes 
the  property  of  another  class  of  creatures — of  animals. 
The  living  animal  consumes  combustible  substances 
54 


HELMHOLTZ  IN  BERLIN 

belonging  to  the  vegetable  world,  and  causes  them  to 
reunite  with  the  oxygen  of  the  atmosphere.  Parallel 
to  this  process  runs  the  work  done  by  animals.  This 
work  is  the  aim  and  end  of  animal  existence.  Plants 
certainly  produce  mechanical  effects,  but  it  is  evident 
that  for  equal  masses  and  times  the  sum  of  the  effects 
produced  by  a  plant  is  vanishingly  small  compared 
with  those  produced  by  an  animal.  While,  then,  in 
the  plant  the  production  of  mechanical  effects  plays 
quite  a  subordinate  part,  the  conversion  of  chemical 
tensions  into  useful  mechanical  effect  is  the  character- 
istic sign  of  animal  life.  In  the  animal  body  chemical 
forces  are  perpetually  expended.  Ternary  and  qua- 
ternary compounds  undergo,  during  the  life  of  the 
animal,  the  most  important  changes,  and  are,  for  the 
most  part,  given  off  in  the  form  of  binary  compounds, 
as  burnt  substances.  The  magnitude  of  these  forces, 
with  reference  to  the  heat  developed  in  these  processes, 
is  by  no  means  determined  with  sufficient  accuracy  ; 
but  here,  where  our  object  is  simply  the  establishment 
of  a  principle,  it  will  be  sufficient  to  take  into  account 
the  heat  of  combustion  of  the  pure  carbon.  When 
additional  data  have  been  obtained,  it  will  be  easy 
to  modify  our  numerical  calculations  so  as  to  render 
them  accordant  with  the  new  facts.' 

(He  then  goes  on  with  calculations.) 

'  If  the  animal  organism  applied  the  disposable  com- 
bustible material  solely  to  the  performance  of  work, 
the  quantities  of  carbon  just  calculated  would  suffice 
55 


HERMANN  VON  HELMHOLTZ 

for  the  times  mentioned.  In  reality,  however,  besides 
the  production  of  mechanical  effects,  there  is  in  the 
animal  body  a  continuous  generation  of  heat.  The 
chemical  force  contained  in  the  food  and  inspired 
oxygen  is  therefore  the  source  of  two  other  forms  of 
power,  namely,  mechanical  motion  and  heat ;  and  the 
sum  of  these  physical  forces  produced  by  an  animal  is 
the  equivalent  of  the  contemporaneous  chemical  process. 
Let  the  quantity  of  mechanical  work  performed  by  an 
animal  in  a  given  time  be  collected  and  converted  by 
friction  or  some  other  means  into  heat ;  add  to  this 
the  heat  generated  immediately  in  the  animal  body  at 
the  same  time,  we  have  then  the  exact  quantity  of 
heat  corresponding  to  the  chemical  processes  that  have 
taken  place. 

4  In  the  active  animal  the  chemical  changes  are 
much  greater  than  in  the  resting  one.  Let  the 
amount  of  the  chemical  processes  accomplished  in  a 
certain  time  in  the  resting  animal  be  .*•,  and  in  the 
active  one  be  x  +y.  If  during  activity  the  same 
quantity  of  heat  were  generated  as  during  rest,  the 
additional  chemical  force  y  would  correspond  to  the 
work  performed.  In  general,  however,  more  heat  is 
produced  in  the  active  organism  than  in  the  resting 
one.  During  work,  therefore,  we  shall  have  *•  plus  a 
portion  of  y  heat,  the  residue  of  y  being  converted  into 
mechanical  effect. 

'  The  maximum  mechanical  effect  produced  by  a 
working  mammal  hardly  amounts  to  one-fifth  of  the 
56 


HELMHOLTZ  IN  BERLIN 

force  derivable  from  the  total  quantity  of  carbon  con- 
sumed. The  remaining  four-fifths  are  devoted  to  the 
generation  of  heat.' 

It  will  be  seen  that  the  doctrine  of  the  conservation 
of  energy  was  of  the  highest  importance  in  physiology, 
as  it  indicated  the  road  to  a  thorough  investigation  of 
the  nutritional  changes  occurring  in  living  matter. 
These  nutritional  changes,  if  in  the  direction  of  the 
upbuilding  of  tissues,  are  also  concerned  in  the  storing 
up  of  energy,  and  if,  on  the  contrary,  they  are  asso- 
ciated with  the  tearing  down  of  tissue,  or,  in  other 
words,  with  chemical  decompositions,  then  energy  is 
set  free  as  mechanical  motion,  heat,  light  or  elec- 
tricity. The  doctrine  also  appeared  to  its  early 
teachers,  at  all  events,  fatal  to  any  vitalistic  theory. 
Time,  however,  has  shown  that  there  still  are  pheno- 
mena connected  with  living  matter  that  are  outside 
the  range  of  even  this  great  principle,  such  as  the  facts 
of  consciousness. 


57 


CHAPTER    VI 

HELMHOLTZ    IN    KONIGSBERG — MEASUREMENT   OF    THE 
RAPIDITY    OF   THE    NERVOUS    IMPULSE 

IN  1849,  m  n's  twenty-ninth  year,  Helmholtz  was 
appointed  to  the  Chair  of  Physiology  and  General 
Pathology  in  the  University  of  Konigsberg.  Here 
he  spent  six  busy  years,  fully  engaged  in  teaching 
and  investigation.  In  the  year  of  his  removal,  1849, 
no  contributions  appeared,  and  we  can  readily  believe 
the  youthful  professor  was  establishing  himself  in  his 
new  sphere  of  duty. 

Early  in  this  year,  also,  he  married  Miss  Olga 
Von  Velten,  of  Potsdam,  who  died  soon  after  his 
settlement  in  Heidelberg  in  1859.  Two  children 
were  born  of  this  marriage — a  daughter,  who  became 
the  wife  of  Professor  Branco,  a  well-known  geologist, 
and  a  son,  who  is  an  engineer  in  Munich,  still  sur- 
vives. Helmholtz  loved  a  quiet  home  life,  with  the 
pleasures  of  congenial  society  and  music,  to  which  he 
was  devoted.  He  was  an  accomplished  pianist,  and 
he  sang  a  little,  but  his  voice  was  not  strong.  As 
his  days  were  devoted  to  scientific  labour,  and  as  he 
58 


HELMHOLTZ  IN  KONIGSBERG 

shunned  publicity  for  the  greater  part  of  his  life,  there 
is  little  of  incident  to  relate. 

The  stream  of  original  papers  began  to  flow  in 
1850,  and  it  increased  in  volume  until  he  moved  to 
Bonn  in  1856.  One  is  astonished  at  the  number  of 
researches  of  first-rate  importance.  Helmholtz  did 
not,  like  many,  lose  time  in  doing  second-rate  work 
that  others,  perhaps,  could  have  done  better.  His 
scientific  instinct  appeared  to  guide  him  often  into 
what  are  termed  virgin  fields.  Thus  he  had  the 
great  satisfaction  of  collecting  the  first  fruits,  and  he 
usually  gathered  so  well  as  to  leave  little  for  others 
who  came  after  him.  Hence  the  researches  and  dis- 
coveries that  were  announced  in  rapid  succession  were 
always  epoch  making,  and  always  in  a  special  sense 
his  own.  During  this  period  he  measured  the  rate 
of  the  nervous  impulse,  he  invented  the  ophthalmo- 
scope, and  he  began  those  investigations  on  colour 
and  sound  that  will  for  ever  be  associated  with  his 
name. 

The  measurement  of  the  rate  of  the  nervous  im- 
pulse was  accomplished  in  1850.  The  problem  was 
to  measure  the  rate  at  which  the  nervous  impulse 
travels  along  a  sensory  nerve,  say  from  the  tip  of  the 
finger  to  the  brain,  or  along  a  motor  nerve,  say  from 
the  brain  to  one  of  the  muscles  of  the  arm.  When 
we  touch  the  finger,  no  time  seems  to  elapse  between 
the  moment  of  touching  and  the  moment  when  we 
are  conscious  of  having  touched  something.  When 
59 


HERMANN  VON  HELMHOLTZ 

we  will  to  move  the  forefinger,  the  commands  of  the 
will  appear  to  be  instantaneously  carried  into  effect. 
This  arises,  however,  from  our  limited  appreciation 
of  shorter  intervals  of  time  than  say  the  one-tenth  of 
a  second,  so  that  if  less  time  elapsed  between  the 
moment  of  touching  the  finger  and  the  moment  of 
the  sensation,  the  two  events  appear  to  be  one.  It 
was  necessary,  therefore,  to  have  some  means  of  re- 
cording the  duration  of  short  periods  of  time,  such 
as  the  short  period  assumed  to  exist  between  the 
moment  of  irritating  a  nerve  and  the  moment  of 
the  contraction  of  the  muscle  supplied  by  it. 

Manifestly  the  subject  could  be  investigated  most 
easily  by  using  the  muscle  of  the  frog  and  the  motor 
nerve  passing  to  it.  Helmholtz  made  use  of  the 
graphic  method  of  recording  the  contraction  of 
muscle,  already  invented  by  him  in  the  form  of  the 
well-known  myograph.  Just  about  this  time  elec- 
trical mechanisms  had  been  introduced  into  practical 
physiology  by  Du  Bois  Reymond,  and  Helmholtz 
made  good  use  of  these  appliances.  He  first  em- 
ployed, as  a  means  of  recording  the  beginning  and  the 
end  of  the  phenomenon,  a  method  devised  by  Pouillet, 
which  consisted  in  noting  the  instant  of  the  move- 
ment of  the  needle  of  a  galvanometer  when  an  in- 
stantaneous current  was  sent  through  the  instrument, 
taking  it  for  granted  that  the  duration  of  the  current 
itself  was  practically  nothing.  Suppose,  then,  that  an 
arrangement  was  made  by  which  a  nerve  could  be 
60 


HELMHOLTZ  IN  KONIGSBERG 

irritated,  say  at  a  distance  of  two  inches  from  the 
muscle,  by  an  electric  current,  which  also  moment- 
arily passed  through  the  galvanometer,  the  move- 
ment of  the  needle  would  indicate  the  instant  when 
the  nerve  was  stimulated.  Helmholtz,  in  the  first 
place,  improved  Pouillet's  method  by  causing  the 
opening  or  closing  shock  from  an  induction  coil  to 
irritate  the  nerve,  either  near  to  the  muscle  or  far 
from  it,  and  he  so  arranged  the  experiment  that 
at  the  moment  of  opening  the  induction  current, 
the  galvanometer  circuit  was  closed,  and  was  again 
opened  by  the  contraction  of  the  muscle  itself.  The 
interval,  then,  between  the  two  swings  of  the  needle 
was  that  between  the  moment  of  irritating  the  nerve 
and  the  moment  of  the  muscular  contraction.  Ar- 
rangements were  then  made  for  irritating  the  nerve 
in  two  successive  experiments  —  first,  close  to  the 
muscle,  and,  second,  at  a  distance  of  say  two  inches 
from  it.  It  was  soon  found  that  the  muscle  did  not 
respond  at  the  instant  the  stimulus  was  applied  to 
the  nerve,  and  that  the  further  away  the  nerve  was 
irritated  the  later  was  the  response.  The  first  dis- 
covery was  that  even  when  the  nerve  was  irritated 
close  to  the  muscle,  a  period  of  something  like  the 
y^j-th  of  a  second  always  elapsed  before  the  muscle 
began  to  contract.  In  other  words,  the  muscle  did 
not  at  once  respond,  but  some  time  was  occupied 
in  those  molecular  changes  that  precede  contraction. 
This  period  was  termed  by  Helmholtz  the  period  of 
61 


HERMANN  VON  HELMHOLTZ 

latent  stimulation.  Edward  Weber  had  endeavoured 
to  draw  a  distinction  between  the  movements  of  in- 
organic and  animal  matter  by  assuming  that  the  latter 
were  instantaneous,  but  the  discovery  of  the  latent 
period  at  once  put  this  distinction  out  of  the  question. 
Helmholtz  next  made  use  of  the  graphic  method, 
introduced  about  that  time  into  physiological  investi- 
gation, and  the  muscle,  by  means  of  a  myograph,  was 
caused  to  write  the  curve  of  its  contraction  on  the 
blackened  surface  of  a  rotating  drum.  About  the 
beginning  of  the  century,  Thomas  Young  showed 
how  time  might  be  recorded  by  marks  made  on  a 
rotating  cylinder,  moving  with  a  uniform  velocity. 
James  Watt  then  applied  the  graphic  method  to 
recording  the  movements  of  the  indicator  of  his 
engine  on  a  cylinder  rotated  by  the  engine  itself. 
Thus  he  obtained  a  curve  representing  variations 
of  steam  pressure  at  different  times.  This  suggested 
to  Ludwig,  then  at  the  beginning  of  his  important 
investigations  into  the  dynamics  of  the  circulation, 
the  conception  of  the  kymograph,  by  which  varia- 
tions of  pressure  in  the  blood  vessels  of  a  living  animal 
were  recorded  on  a  drum  in  a  series  of  waves,  the 
smaller  ones  corresponding  to  the  individual  beats  of 
the  heart,  and  the  larger  to  the  respiratory  move- 
ments. The  myograph  of  Helmholtz,  already  re- 
ferred to  (p.  36),  recorded  the  shortening  of  the 
muscle  with  great  exactitude,  and  thus  Pouillet's 
galvanometrical  method  was  discarded.  He  con- 
62 


HELMHOLTZ  IN  KONIGSBERG 

structed  a  special  myographion,  in  which  a  weight, 
by  centrifugal  action,  liberated  a  spring  that  set 
free  a  simple  mechanism  by  which  a  current  pass- 
ing through  the  primary  coil  of  a  small  induction 
machine  was  opened.  The  shock  thus  obtained  from 
the  secondary  coil  passed  instantaneously  to  the  nerve, 
the  nervous  impulse  was  generated  at  the  point  irri- 
tated, the  impulse  then  travelled  down  the  nerve, 
and  the  muscle  contracted,  writing  its  curve  on  the 
rotating  drum.  In  this  way  two  curves  were  traced 
on  the  cylinder,  one  by  contraction  of  the  muscle 
when  the  nerve  was  stimulated  close  to  the  muscle, 
and  the  other  when  it  was  stimulated  at  a  distance 
from  it.  As  the  nerve,  whether  stimulated  near  or 
far  from  the  muscle,  always  received  the  induction 
shock  at  the  same  moment  when  the  cylinder  had 
attained  its  maximum  velocity,  the  two  curves  did 
not  coincide  at  their  commencement,  the  one  corre- 
sponding to  the  experiment  in  which  the  nerve 
was  stimulated  at  a  distance  being  a  little  behind 
the  one  produced  when  the  nerve  was  stimulated 
near  the  muscle.  Thus  during  the  time  that 
the  nervous  impulse  was  travelling,  say  along  two 
inches  of  nerve,  the  cylinder  had  travelled  a  short 
distance  farther  on — that  is  to  say,  had  rotated  round 
its  axis.  The  distance  between  the  beginnings  of 
the  two  curves  expressed  the  time  occupied  by  the 
nervous  impulse  in  passing  along  a  given  length  of 
nerve.  If  the  velocity  of  the  cylinder  had  been 
63 


HERMANN  VON  HELMHOLTZ 

determined,  then  this  distance  represented  a  certain 
period  of  time. 

By  this  method  a  single  experiment  gave  results 
that  could  only  have  been  obtained,  with  much 
trouble  and  possibilities  of  inaccuracy,  by  a  whole 
series  of  observations  by  Pouillet's  method.  The  ex- 
periments showed  that  in  the  motor  nerves  of  the 
frog  the  velocity  of  the  nervous  impulse  was  only 
about  ninety  feet  per  second  (that  of  a  very  quick 
express  train),  or  about  TVth  part  of  the  velocity  of 
sound  in  air,  a  result  quite  unexpected.  Until  the 
question  was  submitted  by  Helmholtz  to  the  test  of 
experiment,  the  wildest  conjectures  had  been  indulged 
in  by  speculative  physiologists.  Thus  the  iatro- 
mathematicians  of  Montpellier  said  that  the  rapidity 
bore  a  ratio  to  that  of  the  blood  in  the  aorta,  namely, 
in  the  proportion  of  the  diameter  of  the  aorta  to  that 
of  a  nerve  fibre,  a  statement  that  implied  a  velocity 
of  the  nervous  impulse  600  times  more  rapid  than 
light !  Haller  took  as  the  basis  of  his  conjectures 
the  number  of  vibrations  made  by  the  tongue  in  pro- 
nouncing the  letter  R,  and,  by  a  series  of  deductions, 
most  of  them  wide  of  the  mark,'  he  strangely  arrived 
at  a  conclusion  not  very  far  off  what  we  know  to 
be  correct,  namely,  that  the  velocity  was  about  150 
feet  per  second.1  Johannes  Miiller  despaired  of  being 

1  Haller's  Elementa,  t.  iv.,  p,  372 — '  Ego  vero,  cum  haec  mere  theoretica 
sint  experimento  uti  malim,  etsi  minor  summa  prodit.  Ita  invenio 
summam  tamen  celeritatem  esse  muscularis  liquid!  ut  non  minus  quam 
9000  pedes  in  minuto  percurrat.' 

64 


HELMHOLTZ  IN  KONIGSBERG 

able  to  solve  the  problem,  chiefly  because  of  the  short- 
ness of  the  nervous  tracts  in  the  living  animal,  and 
although  he  doubted  the  results  given  by  the  older 
physiologists,  he  thought  that  the  velocity  of  the 
nervous  impulse  must  be  akin  to  that  of  light.  In 
his  great  text-book  he  makes  use  of  the  phrase, 
'  Such  immeasurable  rapidity.'  Again,  he  says, 
'  We  shall  probably  never  attain  the  power  of  meas- 
uring the  velocity  of  nervous  action,  for  we  have 
no  opportunity  of  comparing  its  propagation  through 
immense  space  as  we  have  in  the  case  of  light.' r 
Such  was  the  state  of  opinion  when  Helmholtz  took 
up  the  subject.  His  versatile  intellect  suggested  the 
method  by  which  the  problem  could  be  attacked 
through  the  nerves  and  muscles  of  a  frog,  and,  as 
one  writer  remarks,  <  he  apparently  felt  as  much  at 
home  with  frogs'  nerves  and  muscles,  and  with 
intervals  of  time  of  thousands  of  a  second,  as  he  was 
in  after  years  in  discussing  the  universe  and  the 
immense  measurements  of  time  and  space  involved 
in  a  consideration  of  the  planets.' 

As  already  mentioned,  Du  Bois  Reymond  was 
about  the  same  period  engaged  on  his  researches  on 
animal  electricity.  Following  Matteucci,  but  with 
much  finer  apparatus  and  with  clearer  ideas,  he  had 
shown,  by  means  of  the  galvanometer,  and  specially- 
constructed  non-polarisable  electrodes,  that  the  trans- 
verse section  of  a  resting  muscle  is  negative  to  the 

1  Miiller's  Physiology,  trans,  by  Baly,  vol.  i.,  p.  678. 
E 


HERMANN  VON  HELMHOLTZ 

surface,  as  indicated  by  the  movement  of  the  needle 
of  the  galvanometer  in  a  certain  direction.  This  was 
termed  the  resting  current.  If,  then,  the  muscle  is 
caused  to  contract,  there  occurs  what  DuBois  Reymond 
called  4  the  negative  variation,'  that  is  to  say,  the  needle 
gave;a  swing  towards  zero,  or  even  crossed  to  the  other 
side.  This  negative  variation,  now  called  'the  action 
current,'  is  an  electrical  phenomenon  connected  with 
the  activity  of  the  muscle,  and  the  electric  change 
is  of  sufficient  intensity  to  irritate  the  nerve  of  a 
muscle  preparation,  as  shown  in  Matteucci's  famous 
experiment,  usually  called  the  '  induced  contraction.' 
In  this  experiment  the  nerve  of  a  muscle,  a,  is 
stretched  over  a  muscle  £,  and  if  the  nerve  of  b  is 
irritated  by  an  electric  shock,  not  only  b  but  also  a 
is  thrown  into  contraction,  because  the  c  negative 
variation '  in  muscle  b  irritates  the  nerve  of  muscle  a. 
Helmholtz  attacked  the  time  relations  of  this  problem, 
and  he  thought  he  could  demonstrate  that  the  nega- 
tive variation  occurred  only  in  the  period  of  latent 
stimulation,  and  that  it  was  over  and  gone  before  the 
muscle  began  to  contract.  All  this  work  related  to 
motor  nerves  and  to  the  muscles  and  nerves  of  the 
frog. 

It  seemed  a  more  difficult  problem  to  determine  the 
velocity  in  sensory  nerves.  When  we  touch  a  sensory 
nerve,  the  message  goes  to  the  brain,  but  how  could 
it  be  possible  to  estimate  the  time  it  occupies  in  going 
that  distance,  seeing  the  brain  can  only  respond  by  a 
66 


HELMHOLTZ  IN  KONIGSBERG 

muscular  act  ?  Helmholtz  devised  a  method  by  which 
what  is  called  the  '  reaction  period  '  may  be  computed, 
that  is  the  time  between  the  moment  of  stimulating, 
say  the  skin  of  the  foot  and  the  moment  the  indi- 
vidual makes  a  signal  that  he  has  felt  the  sensation. 
The  reasoning  is  as  follows  :  Suppose  a  sensory  nerve 
to  be  excited  in  the  hand,  the  theory  of  nervous  con- 
duction is  that  a  change  is  propagated  along  the  nerve 
to  the  brain,  and  that  in  the  brain  the  molecular 
changes  occur  which  result  in  a  sensation.  The 
individual  having  the  sensation  may  feel  it  and  make 
no  sign  by  which  anyone  else  might  be  made  aware 
that  he  has  felt  it,  or  the  subject  of  the  sensation 
might,  by  a  muscular  movement,  such  as  the  motion 
of  an  arm,  let  anyone  else  see  that  he  has  felt  the 
sensation.  We  have  no  means  of  knowing  whether 
or  not  an  individual  has  felt  a  sensation  except  by  the 
individual  making  some  kind  of  gesture  or  muscular 
movement.  Now,  it  is  clear  that,  if  we  regard  the 
brain  as  the  seat  of  the  changes  resulting  in  sensation, 
the  nearer  any  stimulated  portion  of  skin  is  to  the 
brain  the  sooner  will  the  brain  feel  and  respond  to 
the  stimulus.  Thus,  if  the  skin  on  the  big  toe  of 
the  right  foot  be  stimulated,  the  effect  of  the  stimulus 
will  pass  to  the  brain  and  there  call  forth  a  sensation  ; 
but  if  the  stimulus  be  applied  to  the  skin  at  the  top 
of  the  thigh,  it  is  evident  the  effect  will  have  to  pass 
along  a  shorter  length  of  nerve,  and  that  the  sensation 
in  the  brain  will  be  aroused  sooner.  If  we  suppose 
67 


HERMANN  VON  HELMHOLTZ 

that  in  each  case  the  individual  who  is  the  subject  of 
the  experiment  indicates  the  moment  he  feels  the 
sensation,  and  that  the  instant  the  stimulus  is  applied 
successively  to  the  skin  on  the  toe  and  on  the  thigh 
is  also  accurately  recorded,  it  is  clear  that  he  will 
signal  the  sensation  of  stimulation  of  the  toe  a  little 
later  than  when  he  signals  stimulation  of  the  skin  on 
the  thigh,  and  that  the  difference  will  indicate  the 
time  required  by  the  change  in  the  nerve  to  pass 
along  the  length  of  the  nerve  from  the  toe  to  the 
thigh.  In  the  observation  it  is  assumed  that  the  time 
required  for  the  changes  in  the  brain,  resulting  in  sen- 
sation and  volition,  for  the  transmission  along  the 
motor  nerve,  and  for  the  muscular  contraction  re- 
quired to  signal,  is  the  same  in  each  experiment. 
Thus,  supposing  the  total  time  between  the  moment 
of  stimulating  and  the  moment  when  the  signal  that 
the  sensation  has  been  felt  and  responded  to  be  JT,  it 
is  clear  that  this  time  is  composed  of  ay  the  time 
required  for  the  passage  of  the  nerve  current  in  the 
first  experiment  from  the  toe  to  the  brain  ;  of  £,  the 
time  required  for  the  changes  in  the  brain  involved  in 
sensation  and  volition  ;  and  of  cy  the  time  required  for 
the  transmission  along  the  motor  nerves  and  for  the 
muscular  contraction  to  move  the  signal — that  is, 
x  =  a  +  b  +  c.  But  if  the  time  between  the  moment  of 
stimulating  the  thigh  to  the  moment  of  signalling  be 
shorter,  and  supposing  that  b  and  c  are  constant,  then 
a  will  vary  according  to  the  length  of  the  nerve. 
68 


HELMHOLTZ  IN  KONIGSBERG 

Suppose  the  difference  of  time  between  the  registra- 
tion of  stimulating  at  the  toe  and  at  the  thigh  to 
be  y,  then  in  the  second  experiment  x  =  a-y  +  b  +  c; 
that  is,  y  =  the  time  occupied  by  the  passage  of  the 
nerve  current  from  the  toe  to  the  thigh.  By  this 
method  the  velocity  of  the  nervous  impulse  in  the 
sensory  nerves  in  man  is  found  to  vary  from  50  to  100 
metres  per  second  (160  to  30.0  feet). 

It  will  be  noted  that  for  motor  nerves  the  obser- 
vations were  made  on  the  frog  and  for  sensory  nerves 
on  man.  The  next  question  Helmholtz  solved  was : 
Is  the  velocity  the  same  or  different  in  the  two  kinds 
of  nerves  ?  By  attaching  the  thumb  to  a  myograph 
and  then  stimulating  near  the  wrist  and  at  the  elbow, 
it  was  found  that  the  muscles  of  the  thumb  contracted 
a  little  later  after  stimulation  at  the  elbow  ;  that  is  to 
say,  the  nervous  impulse  took  some  time  in  travelling 
from  the  elbow  to  the  wrist.  Two  curves  were 
obtained  practically  by  the  same  method  as  was  used 
in  determining  the  rate  in  the  motor  nerve  in  the 
frog,  and  the  velocity  was  found  to  be  the  same  as 
in  the  sensory  nerves  of  man.  In  both  kinds  of 
nerves,  cold  was  found  to  retard  and  heat  to  acceler- 
ate the  velocity  of  transmission. 

These  important  observations  not  only  threw  light 
on  the  question  of  the  transmission  of  the  nervous 
impulse,  but  they  prepared  the  way  for  the  determina- 
tion of  time  relations  in  many  nervous  processes. 
Astronomers  had  long  known  that  in  watching  and 
69 


HERMANN  VON  HELMHOLTZ 

signalling  the  moment  of  the  transit  of  a  star,  there 
were  slight  differences  in  the  observations  made  by 
equally  competent  observers,  differences  apparently 
due  to  individuality.  It  is  said  that  Maskelyne  dis- 
missed an  assistant  because,  in  making  observations, 
he  was  always  behind  his  master  in  point  of  time. 
Bessel  was  the  first  to  recognise  that  the  discrepancies 
were  due  to  the  fact  that  men  feel  and  even  think  at 
different  rates.  As  Hermann  points  out,  the  coinci- 
dence is  striking  that  years  afterwards,  in  the  very 
university  where  Bessel  worked,  Helmholtz  showed 
that  there  was  a  physiological  basis  for  his  conjecture. 
Psycho-physical  investigators  of  later  times,  with  im- 
proved appliances,  have  measured  the  time  occupied 
in  reflex  actions,  and  even  in  those  psychical  operations 
involved  in  choice,  discrimination  and  volition.  Many 
ingenious  instruments  have  since  been  devised,  but 
the  root  idea  of  them  all  may  be  traced  back  to  those 
experiments  of  Helmholtz,  which  originated  the 
methods  of  the  psycho-physical  school  of  investigators. 


70 


CHAPTER    VII 

HELMHOLTZ    IN    KONIGSBERG THE    OPHTHALMOSCOPE 

T_N_.i85l  Helmholtz  conferred  an  inestimable  benefit 
"1  on  humanity,  became  famous  far  beyond  the 
circle  of  his  scientific  friends,  and  handed  his  name 
on  to  posterity  by  the  invention  of  the  ophthalmo- 
scope. Had  he  done  little  else  in  his  long  lifetime,  his 
name  would  never  be  forgotten  ;  and  yet  the  inven- 
tion of  this  instrument  took  its  origin  not  in  any 
profound  investigation,  but  in  the  desire  to  exhibit 
a  physiological  phenomenon  to  his  students.  It  was 
characteristic,  however,  of  his  mind  that  he  was  ever 
receptive  of  new  impressions,  and  when  an  idea 
occurred  to  him,  his  powers  were  brought  persistently 
to  bear  upon  it,  and  if  it  involved  a  problem,  he  had 
no  rest  until  it  was  solved.  The  invention  of  the 
ophthalmoscope  is  a  striking  example,  also,  of  his 
singular  power  of  combining  the  theoretical  with  the 
practical  in  his  daily  life  ;  and  he  could  turn  his  mind 
from  the  contemplation  of  the  mathematical  expres- 
sions of  the  law  of  the  conservation  of  energy,  trac- 
ing in  his  imagination  its  tremendous  consequences, 
to  devising  the  best  method  of  illuminating  the  eye. 
71 


HERMANN  VON  HELMHOLTZ 

At  the  same  time,  although  he  was  practical,  no  one 
more  strongly  denounced  the  pursuit  of  science 
merely  for  its  practical  results.  All  his  physiological 
work,  whilst  of  the  most  thorough-going  kind,  was 
pursued  because  it  was  his  duty  as  a  disciple  of 
science  to  ascertain  the  truth,  and  he  felt  sure  that 
any  practical  advantage  to  medicine,  or  to  science 
in  general,  would  naturally  flow  from  what  to  many 
would  seem  to  be  abstruse  and  theoretical  work.  He 
did  not  require  to  invent  an  ophthalmoscope  to  show 
the  practical  side  of  his  genius  ;  it  was  the  outcome 
of  his  knowledge  of  science,  including  the  anatomi- 
cal structure  of  the  eye  and  the  laws  of  optics.  Yet 
the  invention  of  this  little  instrument,  from  the 
time  of  its  conception  the  daily  companion  of  medical 
men  all  over  the  world — an  instrument,  too,  that  can 
scarcely  be  supplanted  by  any  other — will  keep  his 
memory  green  when  many  of  his  more  elaborate 
works  may  be  forgotten,  or  are  absorbed  in  the  general 
body  of  scientific  truth. 

In  a  speech,  delivered  many  years  after,  Helmholtz 
remarked,  'In  Konigsberg  I  had  to  teach  general 
pathology  and  physiology.  A  teacher  in  a  university 
is  subject  to  excellent  discipline,  in  that  he  is  obliged 
each  year  not  only  to  give  at  least  an  outline  of  the 
whole  of  his  science,  but  also  to  convince  and  satisfy 
the  clear  heads  among  his  hearers,  some  of  whom 
will  be  the  great  men  of  the  next  generation.  This 
necessity  was  most  beneficial  to  myself.  In  prepar- 
72 


HELMHOLTZ  IN  KONIGSBERG 

ing  my  lectures,  I  was  led  to  devise  the  method  of 
measuring  the  velocity  of  the  nervous  impulse,  and 
also  to  the  conception  of  the  ophthalmoscope.  This 
instrument  became  the  most  popular  of  my  scientific 
achievements ;  but  I  have  already  pointed  to  the 
oculists  how  much  good  fortune,  rather  than  any 
personal  merit,  favoured  me  in  its  invention.  -  I  was 
endeavouring  to  explain  to  my  pupils  the  emission  of 
reflected  light  from  the  eye,  a  discovery  made  by 
Briicke,  who  would  have  invented  the  ophthalmo- 
scope had  he  only  asked  himself  how  an  optical 
image  is  formed  by  the  light  returning  from  the 
eye.  In  his  research  it  was  not  necessary  to  ask 
it,  but  had  he  asked  it,  he  was  just  the  man  to 
answer  it  as  quickly  as  I  did,  and  to  invent  the 
instrument.  I  turned  the  problem  over  and  over  to 
ascertain  the  simplest  way  in  which  I  could  demon- 
strate the  phenomenon  to  my  students.  It  was  also 
a  reminiscence  of  my  days  of  medical  study,  that 
ophthalmologists  had  great  trouble  in  dealing  with 
certain  cases  of  eye  disease,  then  known  as  black 
cataract.  The  first  model  was  constructed  of  paste- 
board, eye  lenses,  and  cover  glasses  used  in  the  micro- 
scopic work.  It  was  at  first  so  difficult  to  use,  that 
I  doubt  if  I  should  have  persevered,  unless  I  had  felt 
that  it  must  succeed  ;  but  in  eight  days  I  had  the 
great  joy  of  being  the  first  who  saw  before  him  a 
living  human  retina.' 

It  had  long  been  known  that  the  eyes  of  certain 
73 


HERMANN  VON  HELMHOLTZ 

animals,  more  especially  those  of  birds  of  prey, 
glisten  or  sparkle  in  the  dark.  If  a  cat  is  observed 
entering  a  room  in  shadow,  her  eyes  may  be  seen 
like  little  balls  of  fire,  and  the  red  eyes  of  white  rabbits 
and  other  albinos  are  familiar  to  everyone.  In  1811, 
Pallas  suggested  that  perhaps  one  saw  in  such  cases  the 
naked  -electricity  of  the  retina  (forte  nudum  electricum 
retina  nervts}.  Johannes  Miiller  proved  the  truth  of 
the  view  first  suggested  by  Hassenstein,  that  such  eyes 
do  not  really  emit,  but  only  reflect  light,  and  it 
was  found  that  those  eyes  glistened  most  which  were 
furnished  with  a  special  structure,  called  a  tapetum, 
adapted  for  the  reflection  of  light.  Briicke  was  the 
first  to  show  that  all  eyes  could  be  made  to  glisten  by 
throwing  into  the  eye  the  beam  of  a  lantern  while 
the  rest  of  the  room  was  dark  ;  and  it  is  said  that  at 
night  he  went  to  the  Zoological  Gardens  and  found 
that,  by  taking  up  a  suitable  position,  he  could 
illuminate  the  eyes  of  all  animals.  He  then  tried 
the  experiment  with  the  human  eye,  guided  by  the 
curious  bit  of  information,  that  a  servant  of  his  father 
had  been  dismissed  from  his  situation  because  it  was 
*  uncanny '  to  see  his  eyes  shining  in  the  dark  ! 
The  first  eyes  that  were  illuminated  by  Briicke,  so 
as  to  cause  them  to  shine,  were  those  of  his  friend 
Du  Bois  Reymond.  Soon  afterwards  von  Erlach, 
of  Bern,  who  happened  to  wear  concave  spectacles, 
found  that  by  placing  his  glasses  at  a  particular  angle, 
and  thus  reflecting  light  into  the  eyes  of  his  patient, 
74 


HELMHOLTZ  IN  KONIGSBERG 

he  could  make  them  shine,  an  experiment  very  easily 
repeated.  Then  came  Helmholtz,  who  went  deeper 
into  the  subject,  and  invented  the  instrument.  It 
will  be  seen  how  true  it  was  that  Briicke  came  near 
the  invention,  but  still  there  is  all  the  difference  in 
the  world  between  doing  a  thing  and  not  doing  it. 
The  first  account  of  the  ophthalmoscope  was  pub- 
lished in  1851. J 

In  his  great  work  on  physiological  optics,  the  first 
part  of  which  was  published  in  1856,  Helmholtz 
gives  a  full  account  of  the  whole  subject,  and  as  it  is 
of  extreme  interest  to  medical  men,  I  shall  take  the 
liberty  of  making  full  use  or  it,  sometimes  using  his 
own  words. 

Light  from  the  eye  has  been  observed  from  early 
times  coming  from  the  eyes  of  dogs,  cats  and  other 
animals  who  had  a  tapetum  in  the  fundus  of  the  eye 
— that  is  to  say,  an  area  devoid  of  pigment,  and  covered 
with  thin  and  highly-reflecting  fibres.  In  these  animals 
the  reflection  is  so  intense  as  to  be  easily  perceived, 
even  in  unfavourable  circumstances.  The  ancient 
and  prevalent  opinion  was  that  those  luminous  eyes 
developed  light,  and  that  when  the  animals  were 
irritated,  light  was  evolved  from  their  eyes  under  the 
influence  of  their  nervous  system.  As  the  light  of 
the  eyes  is  best  recognised  when  the  light  comes 
from  behind  the  observer  and  skims  over  his  head,  it 

1  Beschreibung  ernes  Augenspiegeh  -zur  Untersuchung  der  Net%haut  in 
lebenden  Auge.  Berlin,  1851. 

75 


HERMANN  VON  HELMHOLTZ 

is  easy  to  understand  that  a  source  of  light  so  placed 
had  escaped  all  observers.  It  was  also  held  that  the 
eyes  of  white  rabbits  and  of  albinos  had  a  light 
of  their  own.  Prevost,  in  1810,  was  the  first  to  show 
that  the  light  of  the  eyes  of  animals  was  never  seen 
in  complete  darkness,  that  neither  an  effort  of  will 
nor  irritation  caused  it,  and  that  it  was  always  due 
to  the  reflection  of  an  incident  light.  Gruithuisen 
found  the  same  result,  and  further  showed  that  the 
cause  of  the  phenomenon  was  in  the  tapetum  along 
with  the  '  refraction  extraordinaire '  of  the  lens.  He 
also  saw  the  light  in  the  eyes  of  dead  animals.  These 
facts  were  confirmed  by  Rudolphi,  Johannes  Miiller, 
Esser,  Wiedemann  and  Hassenstein.  Rudolphi  ob- 
served that  we  must  look  at  the  eye  in  a  certain 
direction  to  perceive  the  light ;  and  Esser  gave  a 
good  explanation  of  the  changes  of  colour  by  the 
appearance  of  different  coloured  parts  of  the  retina 
which  were  presented  successively  behind  the  pupil. 
Hassenstein,  finally,  found  that  light  was  produced 
when  the  eye  was  compressed  along  its  axis,  and 
supposed  that  in  the  living  animal  luminosity  might 
be  produced  voluntarily  by  a  shortening  of  the  axis  by 
pressure  of  muscles.  The  earlier  observers  recognised, 
then,  luminosity  of  the  eye  as  a  phenomenon  of  re- 
flection without  giving  an  account  of  the  conditions 
that  determined  it. 

In    the  human    eye   luminosity    was    observed    in 
certain  rare  diseases,  in  particular  when  tumours  occu- 
76 


HELMHOLTZ  IN  KONIGSBERG 

pied  the  fundus  of  the  eye.  Behr,  in  1839,  met 
with  a  case  in  which  the  iris  was  absent,  in  which 
there  was  luminosity,  and  noted  that  the  eyes  of 
the  observer  must  regard  those  of  the  patient  in  a 
direction  nearly  parallel  to  that  of  the  incident  rays  j 
such  was  also  the  basis  of  Briicke's  method  of  observ- 
ing the  ocular  light.  In  the  case  of  absence  of  the 
iris,  the  luminosity  was  not  marked  when  the  retina 
was  strongly  illuminated.  Accommodation  was  im- 
perfect in  such  a  case. 

Finally  W.  Gumming1  and  Briicke,  in  1847,  found, 
independently  of  each  other,  the  method  of  rendering 
the  normal  human  eye  luminous,  when  the  observer 
looks  at  it  in  a  direction  nearly  parallel  to  the  incident 
rays.  Briicke  had  already  applied  his  method  to  the 
eyes  of  animals  furnished  with  a  tapetum.  At  last, 
Wharton  Jones,  in  1854,  writes  that  Charles  Babbage 
had  shown  to  him,  about  the  same  time,  a  silvered 
mirror  from  which  a  small  portion  of  the  foil  had  been 
removed,  by  which  light  could  be  thrown  into  the  eye, 
and  at  the  same  time  the  observer  could  look  at  it 
through  the  opening.  This  description  applies  well  to 
the  ophthalmoscope  of  Coccius,  but  as  Babbage  does 
not  appear  to  have  used  lenses  with  his  mirror,  he 
could  not,  in  the  opinion  of  Helmholtz,  clearly  see 
the  retina,  and  probably,  for  that  reason,  he  did  not 
publish  the  discovery.  It  is  evident,  however,  that 
Babbage  almost  invented  the  ophthalmoscope. 

1  Medico-Chirurgical  Trans.,  vol.  xxix.,  p.  284. 

77 


HERMANN  VON  HELMHOLTZ 

The  other  aspect  of  the  question,  why  the  parts  of 
the  retina,  even  when  illuminated,  as  in  the  eyes  of 
animals  having  a  tapetum,  and,  in  albinos,  could  not 
be  distinguished,  has  been  made  the  subject  of  much 
discussion.  The  solution  was  easy.  In  the  beginning 
of  the  eighteenth  century,  Mery  (1704)  had  observed 
that  he  could  see  the  vessels  of  the  retina  of  a  cat 
immersed  in  water,  the  eyes  of  which  were  strongly 
luminous.  La  Hire,  in  1709,  gave  a  correct  explana- 
tion of  this  phenomenon.  He  said  that  it  was  due  to 
a  change  in  the  refraction  of  the  rays  that  made  the 
eye  luminous,  but  he  did  not  attempt  to  give  a  more 
precise  explanation.  It  was  the  same  with  Kussmaul 
in  1845.  He  showed  that  the  retina  became  clear 
and  recognisable  when  the  cornea  and  the  crystallin 
were  removed,  or  when  a  small  portion  of  the 
vitreous  was  removed,  thus  shortening  the  axis  of 
the  eye. 

Helmholtz  was  the  first  to  give  a  complete  account 
of  the  relation  existing  between  the  directions  of  the 
incident  and  emergent  rays,  and  he  gave  the  true 
explanation  of  the  blackness  of  the  pupil.  He  em- 
ployed for  illumination,  plane  unsilvered  glasses,  and, 
to  see  the  retina  better,  concave  lenses.  H.  Reute 
(in  1852),  on  the  other  hand,  was  the  first  to  use  a 
mirror  having  a  hole  in  the  centre,  and  convex  glasses. 
As  the  new  instrument  soon  acquired  great  importance 
in  ophthalmology,  many  ophthalmoscopes  of  different 
forms  have  been  made,  but  they  do  not  involve  any 
78 


HELMHOLTZ  IN  KONIGSBERG 

essentially  new  method  for  illuminating  and  examining 
the  retina. 

Of  the  light  which  strikes  on  the  retina,  one  part  is 
absorbed,  and  that  principally  by  the  black  pigment  of 
the  choroid,  and  the  other  part  is  diffusely  reflected, 
and  returns  from  the  eye  through  the  pupil.  In  ordin- 
ary circumstances,  we  do  not  perceive  the  light  which 
issues  from  the  pupil  ;  this  opening,  on  the  contrary, 
appears  jet  black.  We  must  look  for  the  explanation 
in  the  particular  conditions  of  refraction  in  the  eye, 
and  we  must  also  remember  that,  owing  to  the  pig- 
mentation of  the  eye,  only  a  small  amount  of  light  is 
returned  from  it.  In  all  systems  of  refractive  surfaces 
(lenses),  which  form  an  image  of  a  luminous  point, 
the  rays  may  be  traced  from  the  image  to  the  lumin- 
ous point,  traversing  exactly  the  same  path  as  they 
followed  in  passingfrom  the  luminous  point  totheimage. 
In  other  words,  if  we  put  the  luminous  point  in  the 
position  first  occupied  by  the  image,  the  image  will 
now  be  formed  in  the  place  previously  occupied  by  the 
luminous  point. 

The  result  is  as  follows  : — When  the  human  eye  is 
exactly  accommodated  for  a  luminous  point,  and  forms 
an  exact  image  of  the  point  on  the  retina,  if  we  con- 
sider the  illuminated  part  of  the  retina  as  a  second 
luminous  object,  the  image  formed  by  the  media  of  the 
eye  coincides  exactly  with  the  body  given  ;  so,  in 
front  of  the  eye,  all  the  light  which  returns  from  the 
retina  is  directed  towards  the  luminous  body,  and  it 
79 


HERMANN  VON  HELMHOLTZ 

does  not  pass  by  the  side  of  this  body.  To  receive  a 
part  of  this  light,  it  is  necessary  that  the  eye  of  the 
observer  be  placed  between  the  luminous  body  and  the 
illuminated  eye  ;  this  evidently  cannot  be  done  with- 
out intercepting  the  light  which  goes  to  the  illumin- 
ated eye,  unless  we  employ  a  special  device.  An 
observer,  moreover,  cannot  see  the  light  returned  from 
one  eye  into  the  other  if  the  last  is  exactly  accommo- 
dated for  the  pupil  of  the  observer.  In  these  circum- 
stances, there  is  formed  on  the  retina  of  the  eye  observed 
an  exact  but  dim  image  of  the  pupil  of  the  observer. 
Conversely,  the  media  of  the  eye  under  observation 
forms  precisely  on  the  pupil  of  the  observer  an  exact 
image  of  its  retinal  image,  and,  consequently,  the 
observer  can  only  see  in  the  eye  of  the  other  the 
reflection  of  his  own  black  pupil.  This  explains  how, 
in  ordinary  circumstances,  we  cannot  see  the  fundus 
of  the  eye  we  look  at,  and  how  we  cannot  distinguish 
even  the  parts  which  reflect  the  light  the  most  strongly, 
such  as  the  point  of  entrance,  generally  white,  of  the 
optic  nerve  or  the  blood  vessels.  The  pupil  appears 
black  even  in  albinos  (subjects  in  whom  the  choroid 
has  no  pigment),  if  we  take  the  precaution  to  inter- 
pose a  black  card,  having  a  hole  in  it  the  diameter 
of  the  pupil,  and  thus  prevent  the  light  from 
penetrating  into  the  eye  through  the  sclerotic,  an 
observation  first  made  by  Donders.  It  is,  in  reality, 
the  light  which  passes  through  the  sclerotic  which 
gives  to  the  pupil  of  albinos  its  well-known  red  colour. 
80 


HELMHOLTZ  IN  KONIGSBERG 

In  the  same  way  the  objective  of  a  camera  appears 
black  in  a  dark  room  when  we  throw  on  it  the 
image  of  a  single  flame.  If  the  eye  observed  is, 
on  the  contrary,  neither  exactly  accommodated  for 
the  luminous  body,  nor  for  the  pupil  of  the  observer, 
it  is  possible  that  we  may  perceive  a  little  of  the  light 
which  emerges  from  the  observed  eye,  and  the  pupil 
may  then  appear  to  be  luminous.  It  is  easy  to  see 
that  the  observer  may  receive  light  coming  from  all 
points  of  the  retina  of  the  eye  under  observation,  on 
which  falls  the  diffusive  image  of  his  own  pupil.  If 
we  substitute  a  luminous  disc  for  the  pupil  of  the 
observer,  the  image  of  diffusion  formed  of  this  disc 
in  the  eye  observed  will  coincide  exactly  with  that  of 
the  pupil  of  the  observer,  for  luminous  rays  will  radiate 
from  one  or  many  points  of  the  disc  to  each  point  of 
its  image  of  diffusion  ;  then,  conversely,  the  rays  given 
off  from  each  point  of  the  circle  of  diffusion  will  reach 
one  or  many  points  of  the  luminous  disc,  that  is  to 
say,  the  pupil  of  the  observer.  The  eye  observed 
appears  luminous  when  the  image  of  diffusion  of  the 
pupil  of  the  observer  coincides  with  that  of  a  luminous 
object  in  the  eye  observed.  If  then  we  look  at  an 
eye  by  a  light  from  a  flame  from  which  we  have  shut 
off,  by  an  opaque  screen,  the  rays  that  dazzle  us, 
whether  the  eye  observed  is  accommodated  for  a  distant 
or  near  object,  its  pupil  will  appear  illuminated  in  red. 
During  the  experiment  accommodation  must  be 
at  rest,  if  the  observer  is  far  away,  because  the 
F 


HERMANN  VON  HELMHOLTZ 

least  inexactitude  of  refraction  or  of  accommodation 
will  allow  some  of  the  rays  to  reach  the  observer,  and 
we  are  most  likely  to  succeed  if  the  subject  of  observa- 
tion looks  to  the  side.  The  illumination  is  most 
brilliant  when  the  incident  light  falls  on  the  place  of 
entrance  of  the  optic  nerve,  because  the  white  sub- 
stance of  the  papilla  reflects  light  strongly,  and  be- 
cause, on  account  of  its  diaphanous  structure,  the 
surface  is  not  so  uniform  as  to  receive  a  perfectly  sharp 
image. 

Thus  it  will  be  seen  that  the  invention  of  the 
ophthalmoscope  was  not  a  happy  guess,  but  was  the 
outcome  of  a  careful  sifting  of  the  facts  of  vision. 
In  this  invention,  and  in  its  theoretical  explanation,  we 
have  an  excellent  example  of  Helmholtz's  thorough- 
ness. In  many  of  its  arrangements  the  ophthal- 
moscope has  been  made  more  easy  to  use,  and  the 
observation  of  the  inverted  image  has  its  advantages, 
but  we  have  it  on  the  authority  of  Donders  and 
von  Jaeger,  that  the  instrument  in  its  original  form 
is  optically  complete.  Helmholtz  also  saw  how  the 
instrument  could  be  serviceable  to  ophthalmologists, 
not  only  as  regards  the  examination  of  the  fundus  and 
the  observation  of  changes  in  the  retina,  but  also  as  to 
how  the  refractive  conditions  can  be  accurately  esti- 
mated. In  this  way,  the  degrees  of  myopia  (short- 
sightedness), hypermetropia  (far-sightedness),  and  of 
that  peculiar  condition  known  as  astigmatism  (in 
which,  the  meridians  of  curvature  of  the  refractive 
82 


HELMHOLTZ  IN  KONIGSBERG 

structures,  the  cornea  and  lens,  are  not  the  same),  may 
all  be  determined.  The  invention  of  the  instrument 
was  a  new  era,  not  only  for  ophthalmology,  but  also 
for  practical  medicine,  as  the  retina  may  be  regarded 
as  an  outlying  portion  of  the  brain  ;  an  examination 
of  the  fund  us  of  the  eye  often  gives  the  physician 
information  as  to  pathological  changes  occurring  in 
the  nerve  centres.  Thus  it  is  of  service  in  the  diag- 
nosis of  inflammatory  actions  in  the  brain,  both  acute 
and  chronic  ;  of  changes  in  the  meninges,  or  brain 
coverings  ;  in  locomotor  ataxia  ;  in  the  various  forms 
of  Bright's  disease  ;  and  many  other  maladies. 

The  retina  presents  to  the  observing  eye  the  ap- 
pearance of  a  red-coloured  concave  disc  with  a  whitish 
oval  spot  to  the  inner  side,  where  the  optic  nerve 
enters,  from  which  we  see  branching  the  retinal 
vessels,  the  veins  being  darker  in  colour  than  the 
arteries,  and  in  the  visual  axis  lies  the  yellow  spot, 
which  is  the  most  sensitive  part  of  the  retina.  The 
vessels  of  the  fovea  centralis,  a  minute  depression  in 
the  centre  of  the  yellow  spot,  are  so  fine  as  to  be 
invisible  to  the  naked  eye. 

When  von  Graefe  first  saw  the  fundus  of  the  living 
human  eye,  with  its  optic  disc  and  blood  vessels,  his  face 
flushed  with  excitement,  and  he  cried,  *  Helmholtz  has 
unfolded  to  us  a  new  world  !  What  remains  to  be  dis- 
covered ? '  Before  the  invention  of  the  ophthalmoscope, 
diseases  of  the  fundus,  and  even  disturbances  of  refrac- 
tion and  accommodation  of  the  most  diverse  character, 
83 


HERMANN  VON  HELMHOLTZ 

were  not  differentiated,  and  the  same  treatment  was 
applied  to  all  alike,  often  with  disastrous  results  to 
the  patient.  In  an  eloquent  speech  by  von  Graefe, 
delivered  at  Heidelberg  in  1858,  on  the  occasion  of  the 
Ophthalmological  Congress,  he  said,  l  Under  our  eyes 
we  see  the  mists  disperse,  which,  for  hundreds  of 
years,  have  clouded  the  view  of  our  best  observers, 
and  an  unexampled  field  is  won  for  the  healing  art, 
from  which,  even  already,  after  a  few  brief  years, 
have  been  reaped  most  admirable  fruits.'  Then, 
turning  to  Helmholtz,  he  handed  him,  in  the  name 
of  the  Congress,  a  cup,  on  which  were  inscribed  the 
words  :  *  To  the  creator  of  a  new  science,  to  the 
benefactor  of  mankind,  in  thankful  remembrance  of 
the  invention  of  the  ophthalmoscope.'  Helmholtz 
was  visibly  moved,  and  when  he  went  home  beloved 
lips  said  to  him — '  Better  than  a  decoration  ? '  To 
which  he  replied,  '  Certainly  ;  it  is  a  decoration  on 
the  part  of  competent  judges.' 

Long  afterwards,  on  gth  August  1886,  at  the  fifth 
centenary  of  the  University  of  Heidelberg,  there  was 
another  great  meeting  of  ophthalmologists,  and  Helm- 
holtz was  presented  with  the  von  Graefe  medal,  a 
memorial  of  the  great  ophthalmologist,  awarded  every 
tenth  year  to  the  man  of  whatever  nation  who  has 
rendered  the  greatest  service  to  the  science  of  ophthal- 
mology. Professor  von  Zehender  was  in  the  chair, 
and  in  the  presence  of  many  distinguished  visitors  to 
the  famous  university  on  the  banks  of  the  Neckar, 
84 


HELMHOLTZ  IN  KONIGSBERG 

Donders,  in  a  brilliant  speech,  made  the  presentation. 
After  a  brief  survey  of  Helmholtz's  career,  he  con- 
cluded thus  :  '  And  now,  twenty-eight  years  after 
that  memorable  day,  highly  esteemed  and  honoured 
von  Helmholtz,  I  turn  to  you  in  the  name 
of  that  society  for  which  von  Graefe  then  spoke, 
and  so  to  say,  in  his  name,  in  the  name  of  our 
master  and  patron,  offer  you  the  first  honorary  medal 
instituted  in  his  memory.  May  this  gift  hereafter, 
when  following  the  first  modest  tribute  which  our 
society  long  since  ventured  to  offer  you,  Science 
from  its  highest  circles,  and  your  Emperor,  whom 
you  reverence  and  esteem,  shall  have  heaped  upon 
you  all  the  distinctions  suitable  to  great  endowments, 
associated  with  great  deserts  ;  may  this  gift  still 
remain  to  you  a  gratifying  symbol  of  the  privilege 
you  enjoy  of  living  in  a  generation  that  honours  you 
as  its  benefactor.  May  this  happy  knowledge,  which 
is  not  granted  to  every  man  of  genius,  illumine  with 
its  gentle  light  this  evening  of  your  life,  in  which 
you  may  see  yourself  always  surrounded  in  unfading 
freshness  of  mind  and  body  by  the  love  of  all  that 
are  dear  to  you.' 

Helmholtz  replied,  and  gave  an  interesting  sketch 
of  his  contributions  to  science  in  the  domain  of  physio- 
^ogical  optics.  He  referred  with  great  modesty  to 
the  invention  of  the  ophthalmoscope,  and  to  its  im- 
portant uses  in  the  hands  of  ophthalmologists,  in  the 
following  beautiful  words  :  '  Let  us  suppose  that  up 
85 


HERMANN  VON  HELMHOLTZ 

to  the  time  of  Phidias  nobody  has  had  a  chisel  suffi- 
ciently hard  to  work  on  marble.  Up  to  that  time 
they  would  only  mould  clay  or  carve  wood.  But  a 
clever  smith  discovers  how  a  chisel  can  be  tempered. 
Phidias  rejoices  over  the  improved  tools,  fashions  with 
them  his  God-like  statues  and  manipulates  the  marble 
as  no  one  has  ever  done  before.  He  is  honoured  and 
rewarded.  But  great  geniuses  are  most  modest  just 
in  that  in  which  they  most  excel  others.  That  very 
thing  is  so  easy  for  them  that  they  can  hardly  under- 
stand why  others  cannot  do  it.  But  there  is  always 
associated  with  high  endowments  a  correspondingly 
great  sensitiveness  for  the  defects  of  one's  own  work. 
Thus,  says  Phidias  to  the  smith,  "Without  your  aid 
I  could  have  done  nothing  of  that ;  the  honour  and 
glory  belong  to  you."  But  the  smith  can  only 
answer  him,  "But  I  could  not  have  done  it  even 
with  my  chisels,  whereas  you,  without  my  chisels, 
could  at  least  have  moulded  your  wonderful  works 
in  clay  ;  therefore  I  must  decline  the  honour  and 
glory,  if  I  will  remain  an  honourable  man."  But 
now  Phidias  is  taken  away,  and  there  remain 
his  friends  and  pupils  —  Praxiteles,  Paionios,  and 
others.  They  all  use  the  chisel  of  the  smith.  The 
world  is  filled  with  their  work  and  their  fame.  They 
determine  to  honour  the  memory  of  the  deceased  with 
a  garland  which  he  shall  receive  who  has  done  the 
most  for  the  art,  and  in  the  art,  of  statuary.  The 
beloved  master  has  often  praised  the  smith  as  the 
86 


HELMHOLTZ  IN  KONIGSBERG 

author  of  their  great  success,  and  they  finally  decide 
to  award  the  garland  to  him.  "  Well,"  answers  the 
smith,  "  I  consent  ;  you  are  many,  and  among  you 
are  clever  people.  I  am  but  a  single  man.  You 
assert  that  I  singly  have  been  of  service  to  many  of 
you,  and  that  many  places  teem  with  sculptors  who 
have  decked  the  temples  with  divine  statues,  which, 
without  the  tools  that  I  have  given  you,  would  have 
been  very  imperfectly  fashioned.  I  must  believe  you, 
as  I  have  never  chiselled  marble,  and  I  accept  thank- 
fully what  you  award  to  me,  but  I  myself  would  have 
given  my  vote  to  Praxiteles  or  Paionios." ' 


CHAPTER    VIII 

HELMHOLTZ     IN     K.5NIGSBERG  THE     MECHANISM     OF 

ACCOMMODATION FIRST  VISIT  TO  ENGLAND 

FROM  1851  to  1856,  when  he  went  to  Bonn, 
Helmholtz  was  mainly  engaged  in  researches 
in  physiological  optics.  Now  and  again  he  entered 
on  electrical  problems,  two  papers  appearing  in  1851 
on  the  induction  coil.  In  1852  he  gave  an  interest- 
ing rlsumi)  characterised  by  much  critical  acuteness,  of 
the  progress  of  electro-physiology,  or  animal  electri- 
city, up  to  that  date.  It  was  in  1851  that  he  began 
the  systematic  examination  of  the  eye,  both  as  regards 
its  anatomy  and  its  physical  constants,  an  examination 
that  culminated  in  his  great  work  on  physiological 
optics  ;  and  it  was  also  in  1852  that  he  invented  the 
ophthalmometer.  In  this  year  he  also  wrote  an  im- 
portant paper  on  the  theory  of  heat  as  applied  to 
living  beings  ;  a  paper  dealing  with  the  relation  of  heat 
to  work  appeared  in  1855.  Further,  it  was  in  1852 
that  problems  of  a  psychological  nature  first  occupied 
his  attention.  The  publication  of  the  results  of  his 
investigations  into  these  problems  first  began  in  1852 
with  a  short  but  fundamental  paper  on  the  nature  of 
88 


HELMHOLTZ  IN  KONIGSBERG 

sensation,  and  then  there  followed  in  rapid  succession 
a  series  of  papers  on  the  phenomena  of  colour.  The 
first  announcement  of  research  into  acoustical  ques- 
tions was  also  made  in  1852,  a  subject  which  occupied 
much  of  his  attention  till  1863,  when  he  published 
his  great  work  on  Sensations  of  Tone  as  the  Physio- 
logical Basis  of  Music,  a  work  that  may  fitly  be  called 
the  Prlncipia  of  acoustics.  It  was  probably  in  Konigs- 
berg  that  his  genius  burst  forth  in  all  its  splendour, 
although  it  had  not  yet  reached  its  zenith,  and  this 
period  was  characterised  by  intense  mental  activity, 
as  indicated  both  by  the  far-reaching  nature  of  the 
problems  he  attacked,  and  by  the  success  with  which 
he  achieved  at  least  their  partial  solution. 

The  University  of  Konigsberg  may  well  be  proud 
of  her  famous  professor.  The  distinguished  man  who 
now  occupies  the  chair  of  physiology  there,  Professor 
Ludwig  Hermann,  in  an  address  on  Helmholtz, 
remarks  with  pardonable  pride  :  '  In  a  little  room  in 
the  anatomical  department,  which  was  his  workshop, 
originated  the  myographion,  the  ophthalmometer,  and 
the  ophthalmoscope.  His  models  were  first  con- 
structed with  his  own  hands,  chiefly  with  wire,  cork, 
and  sealing-wax,  and  then  they  were  completed  by 
Rekoss.'  In  these  days  of  palatial  laboratories  spring- 
ing up  all  over  the  world  in  connection  with  each 
department  of  science,  it  is  well  not  to  forget  that 
some  of  the  greatest  results  in  science  have  been 
gained  in  humble  rooms  and  with  simple  appliances. 
89 


HERMANN  VON  HELMHOLTZ 

Neither  the  most  splendid  buildings,  fitted  with  the 
most  modern  appliances,  nor  the  endowment  of 
research,  however  wisely  conceived,  will  compensate 
for  the  absence  of  genius.  The  living  spirit  must  be 
the  propelling  force,  and  whilst  it  is  reasonable  that 
every  facility  for  research  should  be  afforded,  a  view 
which  is  now  recognised  in  every  civilised  country, 
and  mostly  by  those  nations  that  form  the  vanguard 
of  progress,  there  still  remains  the  fact  that  in  Science 
as  in  Art  the  great  investigator,  like  the  great  artist,  is 
born,  not  made. 

Helmholtz,  like  all  hard  workers,  needed  periods  of 
comparative  rest,  and  he  was  wont  usually  to  betake 
himself  to  the  mountains  and  valleys  of  Switzerland. 
The  year  1854  is  memorable  from  the  occurrence  of 
his  first  visit  to  England,  and  in  a  letter  written  to  his 
friend  Ludwig,1  after  his  return,  we  get  a  glimpse 
into  his  first  impressions  : — 

*  KoNIGSBERG,  2,  VI.    54. 

1  DEAR  LUDWIG, — England  is  a  great  land,  and  one 
feels  there  what  a  magnificent  and  splendid  thing  civili- 
sation is,  and  how  the  minutest  conditions  of  life  bear 
its  impress.  In  comparison  with  London,  Berlin  and 
Vienna  are  mere  villages.  To  describe  London  is 
impossible ;  it  must  be  seen  with  one's  own  eyes 
before  one  can  attempt  to  form  an  estimate  of  it.  A 

1  For  this  letter  I  am  indebted  to  my  friend  Professor  Hugo  Kronecker, 
of  Bern,  whose  Life  of  Helmholtz,  is   eagerly  expected.     It   is  understood 
that  many  letters  have  been  placed  at  his  disposal. 
90 


HELMHOLTZ  IN  KONIGSBERG 

visit  to  London  marks  an  epoch  in  one's  life  ;  after  such 
a  visit,  one  learns  to  judge  human  actions  on  a  scale 
hitherto  unknown.  I  have  been  very  unfortunate  in 
meeting  scientific  men,  missing  Rankine,  Brewster, 
Joule,  Thomson,  and  Wheatstone,  but  with  Faraday, 
Stokes,  Sabine,  Grove,  Airy,  Bence  Jones,  Andrews 
the  chemist,  Hamilton  the  mathematician,  and  many 
others  of  lesser  importance,  I  have  had  better  luck. 
These  men  seem  to  be  as  generous  as  Swiss  tourists 
are  odious  ! 

*  Bence  Jones  is  "  a  man  among  men,"  as  we  say  in 
Berlin.  He  invited  me  to  his  villa  at  Folkestone,  on 
the  sea  coast,  where  I  met  Du  Bois  Reymond  and  his 
wife.  Our  friend  has  become  quite  an  Englishman. 
I  was  received  there  as  heartily  as  if  I  had  been  an  old 
friend.  I  spent  three  weeks  sight-seeing  in  London, 
and  when  I  left  it  for  the  meeting  (of  the  British 
Association)  in  Hull,  I  had  not  even  seen  the  half  of 
it.  The  organisation  of  the  meeting  at  Hull  greatly 
interested  me.  There  was  not  much  scope  for 
physics,  chemistry,  and  such  like  sciences,  in  which  a 
man  must  work  by  himself,  and  the  leaders  of  these 
sciences  kept  in  the  background.  For  other  sciences, 
however,  such  as  meteorology,  ethnology  and  geology, 
where  there  must  be  co-operation  among  many  ob- 
servers, the  meetings  (of  sections)  were  of  great 
importance.  There  were  over  800  members,  and,  in 
addition,  250  ladies  who  came  to  listen.  As  a 
foreigner,  I  was  the  guest  of  Dr  Cooper,  a  physician, 


HERMANN  VON  HELMHOLTZ 

who  entertained  me  most  hospitably.  I  then  spent 
eight  days  in  Scotland,  to  feast  on  nature.  Edinburgh 
is  a  jewel  among  cities.  The  Scotch  Highlands  have 
a  peculiar  majesty,  from  their  proximity  to  the 
Atlantic  Ocean  ;  but  they  are,  on  the  whole,  barren 
and  monotonous,  and  not  to  be  compared  with  the 
Alps.  I  saw  Fingal's  Cave  in  beautiful  weather,  then 
unceasing  rain  compelled  me  to  return.  I  travelled 
home  via  Hull  and  Hamburg,  and  arrived  with  a  very 
empty  purse.  My  health  has  greatly  benefited  by 
the  trip,  but  my  teeth  troubled  me  on  the  journey, 
and  made  for  a  time  my  physiognomy  asymmetrical.' 

In  after  years  Helmholtz  paid  not  a  few  visits  to 
this  country,  and  more  especially  to  his  friend  of  many 
years,  Lord  Kelvin.  Between  these  distinguished  men, 
the  foremost  in  their  time  in  physical  science,  there 
always  existed  the  warmest  friendship.  Often  differing 
on  scientific  questions,  each  had  admiration  and  respect 
for  the  powers  and  achievements  of  the  other. 

To  return  to  the  physiological  work  of  Helmholtz 
during  the  early  fifties,  there  can  be  no  doubt  the  re- 
searches on  the  mechanism  of  accommodation  and  on 
sensations  of  colour  were  of  the  first  importance.  His 
singular  combination  of  anatomical,  physiological,  phy- 
sical, and  mathematical  knowledge  fitted  him  specially 
for  this  work.  Up  to  his  day  no  one  had  appeared  like 
him  in  this  respect,  and  it  may  be  questioned  if  any- 
one now  exists  who  can  be  placed  on  the  same  platform 
92 


HELMHOLTZ  IN  KONIGSBERG 

with  Helmholtz,  much  as  many  physiologists,  especially 
in  Germany,  now  cultivate  physics  and  mathematics. 

The  ophthalmometer,  an  instrument  of  too  technical 
a  character  to  be  here  described,1  enabled  Helmholtz 
to  determine  many  of  the  optical  constants  of  the  eye, 
more  especially  as  to  the  radii  of  curvature  of  the  re- 
fractive surfaces,  the  cornea  and  lens.  He  was  also 
able  to  solve  the  interesting  problem  as  to  the  focussing 
or  accommodating  mechanism  of  the  eye,  by  which  it 
adapts  itself  for  distinct  vision  within  a  certain  range. 

In  the  normal  eye  parallel  rays  coming  from  infinity 
are  brought  to  a  focus  on  the  retina,  and  a  distinct 
image  is  formed.  When  rays  are  not  brought  accu- 
rately to  a  focus  on  the  retina,  the  image  is  indistinct, 
by  the  formation  of  circles  of  diffusion  around  its 
margin.  It  is  evident  that  if  an  object  be  brought 
too  close  to  the  eye  for  the  refractive  media  to  focus 
it  on  the  retina,  circles  of  diffusion  will  be  formed, 
with  the  result  of  causing  indistinctness  of  vision, 
unless  the  eye  has  some  power  of  altering  its  length 
or  the  curvature  of  its  refractive  surfaces.  That 
the  eye  has  some  such  power  of  accommodation  is 
proved  by  the  observation  that  if  we  look  through  the 
meshes  of  a  net  (the  net  say  3  feet  from  the  eye)  at 
a  distant  object,  we  cannot  see  both  the  meshes  and 
the  object  with  equal  distinctness  at  the  same  time. 
At  one  moment  the  meshes  will  be  seen  distinctly 

1  Fully  described  in  Appendix  D,  p.  718,  of  my  Outlines  of  Physiology. 
Glasgow,  1878. 

93 


HERMANN  VON  HELMHOLTZ 

and  at  the  next  the  distant  object.  Again,  if  we 
persistently  look  at  objects  close  to  the  eye,  say 
within  6  inches,  there  is  a  sense  of  effort  and  the 
eye  becomes  fatigued.  The  range  within  which  the 
accommodating  mechanism  works  is,  in  the  normal 
eye,  from  65  metres  (about  70  yards),  the  so-called 
punctum  remotum^  to  -^th  metre  (20  centimetres,  say 
10  inches),  the  punctum  proximum.  Beyond  65  metres 
rays  emanating  from  an  object  may  be  practically 
regarded  as  parallel,  and  they  will  be  focussed  on  the 
retina  without  effort ;  from  65  metres  to  ^th  metre 
the  accommodating  mechanism  comes  into  play  so  as 
still  to  bring  the  more  divergent  rays  to  a  focus  on 
the  retina,  and  thus  secure  distinct  vision ;  and 
lastly,  within  a  distance  of  4th  metre  (except  in  juvenile 
life)  the  accommodating  mechanism  ceases  to  act.  the 
rays  that  enter  the  pupil  are  now  too  divergent  to  be 
focussed  on  the  retina,  and  there  is  blurred  vision. 
If  we  cut  off  the  more  divergent  rays  by  looking  at 
the  near  object  (say  2  inches  from  the  eye)  through 
a  hole  in  a  card,  then  we  can  see  the  object  dis- 
tinctly as  we  now  use  the  central  pencils  of  rays 
which  may  be  slightly  divergent  or  nearly  parallel. 
The  pupil,  the  diameter  of  which  is  lessened  by  con- 
traction of  the  iris,  serves  the  same  purpose.  Con- 
sequently, when  we  look  at  a  near  object  the  pupil 
contracts.  The  question  arises,  how  is  this  wonderful 
mechanism  carried  out  ? 

If  we  hold  a  lighted  candle  in  front,  and  a  little  to 
94 


HELMHOLTZ  IN  KONIGSBERG 

the  side  of  a  living  eye,  three  reflections,  or  little 
specks  of  light,  may  be  seen  in  the  eye.  The  brightest 
one,  an  erect  image,  is  on  the  anterior  surface  of  the 
cornea  ;  the  next,  also  erect,  but  much  less  distinct, 
is  on  the  anterior  surface  of  the  crystalline  lens  ;  and 
the  third,  extremely  faint  and  difficult  to  see,  is 
inverted  and  comes  on  the  posterior  surface  of  the 
lens.  The  one  on  the  anterior  surface  of  the  cornea 
has  no  doubt  been  long  familiar,  the  '  light  of  the  eye,' 
represented  by  artists  in  a  portrait  by  the  little  speck 
of  yellowish  white  paint.  The  next,  on  the  anterior 
surface  of  the  lens,  was  long  ago  observed  by  Sanson, 
who  looked  for  it  in  connection  with  the  appearance  of 
cataract ;  while  the  third  was  first  discovered  by  one  of 
the  older  physiologists — Purkinje,  who  detected  many 
things,  so  that  his  name  appears  in  every  physiological 
text-book.  A  Dutch  observer,  Cramer,  made  the 
happy  observation  that  if  the  eye  suddenly  transfers 
its  gaze  from  a  distant  to  a  near  object,  the  middle 
image  moves  nearer  the  most  anterior  image,  and  at 
the  same  time  becomes  smaller.  As  this  image  is  a 
reflection  from  the  anterior  surface  of  the  lens,  and 
as  an  image  on  a  more  convex  lens  is  always  smaller 
than  one  on  a  less  convex  surface,  it  will  be  evident 
that  when  the  eye  focusses  on  the  retina  the  more 
divergent  rays  that  come  from  a  near  object,  it 
changes  its  curvature  and  becomes  more  convex. 
Accommodation,  then,  consists  in  an  increasing 
convexity  of  the  lens,  beginning  when  the  eye  looks 
95 


HERMANN  VON  HELMHOLTZ 

at  an  object  at  a  distance  of  65  metres  and  ending 
when  the  near  point  is  reached  at  a  distance  of 
^th  metre. 

Before  these  observations  were  made,  the  most 
diverse  views  had  been  advanced  by  physiologists  as 
to  the  mechanism  of  accommodation.  Some  denied 
that  any  change  took  place  in  the  refractive  media, 
and  also  that  any  change  was  necessary  ;  others,  that 
a  change  took  place  in  the  form  of  the  globe  of  the 
eye,  the  organ  becoming  compressed  by  the  muscles 
that  move  it,  so  that  it  became  slightly  longer  for 
near  objects  than  for  those  at  a  great  distance  ;  others, 
that  the  contraction  of  the  pupil  that  takes  place 
when  we  look  at  a  near  object  is  sufficient  to  explain 
the  mechanism  ;  others,  that  there  was  a  change  in 
the  curvature  of  the  anterior  surface  of  the  cornea  ; 
others,  that  the  lens  was  displaced  backwards  or  for- 
wards by  the  mucular  iris ;  while,  finally,  the  true 
explanation,  verified  by  the  facts  already  stated,  had 
many  supporters  from  the  time  of  Descartes  down- 
wards. The  first  correct  observation  was  undoubtedly 
made  by  Thomas  Young.1  His  experiment  consisted 
in  looking  through  wire  gauze  at  a  luminous  point. 
An  image  of  diffusion  is  then  seen,  traversed  by 
straight  lines,  which  are  the  shadows  of  the  wires  of 
the  gauze.  These  lines  are  quite  straight  when  we 
look  at  a  distant  object,  but  they  appear  to  be  curved 

1  Phil.  Tram.  1801,  vol.  i.,  p.  23,  also  vol.  i.  of  Young's  Works, 
edited  by  Peacock.  London,  1855. 


HELMHOLTZ  IN  KONIGSBERG 

at  their  extremities  if  the  eye  is  directed  to  an  object 
close  at  hand,  a  result  that  can  only  be  explained  by 
supposing  that  the  lens  becomes,  in  the  latter  case, 
more  convex.  This  experiment,  difficult  of  execution, 
excited  the  admiration  of  Helmholtz,  who  always 
regarded  Young  as  a  man  before  his  time,  and  one  of 
the  greatest  of  English  philosophers.  Max  Langen- 
beck,1  about  1849,  came  near  the  true  explanation, 
but  it  was  reserved  for  Cramer  to  complete  the  dis- 
covery. He  observed  the  image  of  a  flame,  reflected 
from  the  anterior  surface  of  the  lens,  by  means  of  a 
short  focus  telescope,  and  noticed  the  essential  fact 
that  the  image  became  smaller  when  the  eye  was 
directed  to  a  near  object. 

Helmholtz,  unacquainted  at  the  time  with  the 
work  of  Langenbeck  and  Cramer,  now  took  up  the 
question,  and,  with  his  usual  thoroughness,  went  to 
the  bottom  of  it.  He  arrived  at  the  same  conclusions 
as  Cramer,  but  he  went  much  farther.  Here,  again, 
there  was  no  question  of  priority.  When  Cramer's 
work  was  brought  under  his  notice  by  the  writings 
of  his  friend  Donders,  who  rescued  Cramer  from 
oblivion,2  Helmholtz  at  once  recognised  his  merits. 
Donders,  in  the  speech  already  referred  to,  said : 
'If  it  be  a  satisfaction  to  me  to  venture  to  claim 
the  first  for  my  countryman,  D.  A.  Cramer,  I  must 

1  Kl'mische  Beitrage.     Gbttingen,  1849. 

2  Tijdschrift  der  Maatschappy  -voor  Geneeskunde,  1851,  vol.  xi.,  p.  15  ; 
also  Nederlandtch  Lancet,  2  i.  p.  529,  1851-2. 

G 


HERMANN  VON  HELMHOLTZ 

not  omit  to  state  that  Helmholtz  shortly  afterwards 
arrived  independently  at  the  same  result.  With  a 
noble  modesty,  for  which  I  thank  him,  he  declared 
himself  convinced,  after  an  examination  of  the  papers 
sent  to  him,  that  the  enigma  of  accommodation,  upon 
which  so  many  enquirers  had  exhausted  their  in- 
genuity, was  in  reality  solved  as  to  the  main  point, 
and  very  little  now  remained  for  him  to  do  in  the 
researches  he  contemplated.'  Helmholtz,  in  the  first 
instance,  contrived  a  little  instrument,  the  phakoscope, 
by  which  the  images  in  the  eye  may  be  seen  even 
better  than  in  a  darkened  room.  Then  he  invented 
an  instrument  for  the  purpose  of  measuring  the  size 
of  any  image  reflected  from  a  curved  surface.  This, 
one  of  the  most  ingenious  devices,  is  known  as  the 
ophthalmometer.  It  depends  essentially  on  the  displace- 
ment to  one  side  caused  by  holding  a  plate  of  thick 
glass  obliquely  in  front  of  any  object.  The  object 
may  thus  be  displaced  through  a  distance  equal  to  its 
breadth,  and  the  angular  movement  may  be  read  off 
on  a  graduated  disc  attached  to  the  axis  rotating  the 
glass  plate.  Helmholtz  used  two  plates,  rotating  in 
opposite  directions,  so  that  the  object  was  displaced 
both  to  the  right  and  left,  and  the  image  was  viewed  by 
a  short  focus  telescope  placed  behind  the  plates.  The 
instrument  may  be  graduated  empirically,  or  it  may 
be  used  with  the  aid  of  a  formula  by  which  the  size 
of  the  object  may  be  readily  calculated.  An  image 
is  first  obtained  by  throwing  into  the  eye  reflec- 
98 


HELMHOLTZ  IN  KONIGSBERG 

tions  from  three  little  mirrors  placed  on  a  rod  in  the 
same  plane  as  that  of  the  eye  under  examination.  These 
little  specks  of  light  are  thus  seen  in  a  straight  line, 
reflected  on  the  anterior  surface,  say,  of  the  cornea, 
and  the  distance  between  the  two  most  distant  specks 
is  the  breadth  of  the  image  ;  the  third  little  speck 
is  exactly  midway  between  the  other  two.  The 
ophthalmometer  is  then,  from  a  suitable  distance, 
directed  towards  the  eye,  and  the  plates  are  rotated 
until  the  object  divides  into  two,  and  the  displace- 
ment is  continued  until  there  has  been  an  apparent 
movement  through  the  breadth  of  the  object.  The 
angular  displacement  is  then  noted,  and,  as  already 
stated,  by  the  use  of  a  formula,  the  size  of  the  re- 
flected image  may  be  calculated  in,  say,  millimetres,  or 
fractions  of  a  millimetre.  Finally,  if  the  size  of  the 
real  object  (the  distance  between  the  two  mirrors 
farthest  apart  on  the  rod),  the  distance  of  the  plate 
from  the  eye  (the  vertex  of  the  cornea),  and  the  size 
of  the  reflected  image  (as  measured  by  the  ophthalmo- 
meter), are  given,  it  is  easy  to  calculate  the  radius 
of  curvature  of  the  reflecting  surface.  Helmholtz, 
by  means  of  this  beautiful  arrangement,  was  able  to 
show  ( i )  that  the  radius  of  curvature  of  the  cornea  for 
near  and  distant  objects  does  not  change  ;  (2)  that  the 
length  of  the  radius  of  curvature  of  the  anterior  sur- 
face of  the  lens,  when  the  eye  looks  at  an  object  far 
away,  is  10  millimetres,  and  is  only  6  millimetres 
when  the  eye  looks  at  a  near  object,  that  is  to  say, 
99 


HERMANN  VON  HELMHOLTZ 

in  the  latter  case,  the  anterior  surface  of  the  lens 
becomes  more  convex  ;  (3)  that  the  posterior  surface 
of  the  lens  also  becomes  slightly  more  convex,  as 
for  near  objects  the  radius  of  curvature  becomes 
shorter  (5-5  mm.)  than  for  distant  objects  (6  mm.)  ; 
(4)  that  when  we  look  at  a  near  object,  the  distance 
of  the  vertex  of  the  cornea  from  the  anterior  surface 
of  the  lens  becomes  shorter  (3-3  mm.)  than  for  a 
distant  object  (3-7  mm.)  ;  and  that  during  accommo- 
dation the  lens  becomes  thicker,  being  3-8  mm.  in 
thickness  for  a  distant  object  and  4-3  mm.  for  a  near 
object,  or  from,  approximately,  a  £th  to  a  ^th  of  an 
inch.  This  amount  of  change  is  quite  sufficient  to 
bring  to  a  focus  on  the  retina  rays  of  light  emana- 
ting from  an  object  looked  at  within  the  limits  of 
accommodation. 

It  only  remained  to  explain  how  the  curvature  of 
the  lens  can  thus  be  changed,  and  here  Helmholtz 
brought  his  anatomical  knowledge  to  bear  upon  the 
question.  Thomas  Young,  and  many  of  the  older 
observers,  thought,  erroneously,  that  the  lens  was  a 
muscular  structure.1  C.  Weber,  about  1850,  electric- 
ally excited  the  eye,  and  observed  the  anterior  surface 
of  the  lens  moving  towards  the  cornea.  Cramer 
also  electrically  irritated  the  eye,  and  concluded  that 
a  change  of  form  was  produced  by  contractions  of 
muscular  structures  in  the  eye  itself,  and  he  attributed 

1  Diiyuititionet  quae  ad  facultatem  oculum  accommodandi  sfectant.  Mar- 
burg, 1850,  p.  31. 

100 


HELMHOLTZ  IN  KONIGSBERG 

the  movements  chiefly  to  the  iris.  This  muscular 
structure  contains  both  circular  and  radiating  fibres. 
As  a  matter  of  fact,  distinct  radiating  fibres  cannot 
be  seen  in  microscopical  preparations.  Suppose  both 
circular  and  radiating  fibres  contracted  simultaneously, 
then,  according  to  Cramer,  the  circular  fibres  offered 
resistance  to  the  contraction  of  the  radiating  fibres, 
and  thus  the  parts  of  the  lens  behind  them,  that  is 
near  the  margins,  were  compressed,  while  the  central 
part  of  the  lens,  meeting  with  no  resistance  behind 
the  pupil,  was  pressed  forward.  Donders  next 
attached  importance  to  the  fringe  of  elastic  tissue 
on  the  inner  wall  of  the  canal  of  Schlemm,  from  which 
both  the  fibres  of  the  iris  and  of  the  ciliary  muscle 
appear  to  originate.  The  latter  muscle  is  a  fringe 
of  muscular  tissue,  the  fibres  of  which  radiate  back- 
wards, and  are  attached  to  the  ciliary  processes  of  the 
choroid  or  vasculo-pigmentary  coat  of  the  eye.  It 
lies  near  the  zonule  of  Zinn,  and  was  at  one  time 
termed  corpus  ciliare^  the  ciliary  body.  Briicke  de- 
scribed it  in  the  following  words  :  c  The  muscle  is 
very  easy  to  find,  as  it  is  nothing  else  than  the  light 
grey  ring  which  one  finds  on  the  outer  surface  of 
the  anterior  part  of  the  choroid  after  separation  of 
the  sclerotic,  and  which  has  up  till  now  played  so 
unhappy  a  part  in  anatomy  under  the  names  of 
ligamentum  ciliare^  orbicularis  ciliarisy  circulus  allans, 
ganglion  ciliare,  etc.'  It  may  now  be  well  named  the 
tensor  choroidei,  or,  as  Donders  suggests,  the  ?nusculus 
101 


HERMANN  VON  HELMHOLTZ 

Briickianus^  in  honour  of  its  discoverer.  Helmholtz 
took  up  the  matter  at  this  point,  and  made  the  happy 
suggestion,  which  is  now  universally  accepted  as  the 
true  explanation,  that  in  accommodation  the  fibres 
of  the  ciliary  muscle  contract  and  tend  to  draw  the 
ciliary  processes  of  the  choroid  forward.  Passing  in 
close  proximity  to  these  processes,  and  connected  with 
them,  is  a  thin  transparent  membrane,  the  hyaloid 
membrane,  which  lines  the  posterior  chamber  of  the 
eye.  Anteriorly  this  membrane  divides  into  two 
layers,  one  passing  before  and  the  other  behind  the 
lens,  forming  what  is  termed  its  capsule.  The  lens 
is  thus  bound  down,  as  it  were,  by  its  capsule,  more 
especially  by  the  portion  of  it  passing  over  its  anterior 
surface.  When,  then,  the  ciliary  processes  are  pulled 
forward  by  the  ciliary  muscle,  the  tension  of  the  layer 
of  the  capsule  in  front  of  the  lens  is  diminished,  and 
the  anterior  surface  of  the  lens  bulges  forward  by  its 
elasticity.  There  are  certain  circular  fibres  of  the 
ciliary  muscle  that  also  assist  in  this  beautiful 
mechanism.  When  the  eye  is  again  directed  to  a 
distant  object,  the  fibres  of  the  ciliary  muscle  relax, 
and  the  lens  is  flattened  by  the  pressure  of  the 
capsule. 

Finally,  and  to  complete  the  demonstration,  Helm- 
holtz showed,  that  to  accomplish  accommodation,  no 
other  change  in  the  eye  is  necessary,  and  he  described 
an  imaginary  or  schematic  eye,  slightly  differing  from 
the  eye  of  Listing,  and  for  this  eye  he  calculated  the 


HELMHOLTZ  IN  KONIGSBERG 

optical  constants  as  they  exist  for  near  and  distant 
vision  in  accommodation.  He  then  found  that  the 
positions  of  these  constants,  such  as  the  position  of 
the  anterior  focus,  the  positions  of  the  nodal  and 
principal  points,  and  the  posterior  focus,  varied  for 
near  and  far  vision  as  they  would  do  if  the  only 
changes  occurring  during  the  mechanism  were  in  the 
curvatures  of  the  anterior  and  posterior  surfaces  of 
the  lens,  as  ascertained  by  experiment  and  measure- 
ment by  the  ophthalmometer.  So  the  question  was 
finally  settled.  The  discovery  of  the  part  played 
by  the  lens  in  accommodation  is  one  of  the  greatest 
triumphs  in  modern  physiology.  Lucid  mathematical 
and  experimental  proofs  have  been  given  of  its 
correctness,  and  all  other  theories  have  been  entirely 
abandoned. 


103 


CHAPTER    IX 

HELMHOLTZ    IN    K.ONIGSBERG ANIMAL    ELECTRICITY 

IN  after  life  Helmholtz  made  important  mathe- 
matical and  physical  contributions  to  the  theory 
of  electrical  actions,  and  it  is  interesting  to  observe, 
while  the  fact  is  in  keeping  with  the  plan  of  his 
whole  career,  that  he  was  led  into  this  path  from 
the  side  of  physiology.  Before  he  left  Berlin,  and 
while  he  was  in  Konigsberg,  his  friend  Du  Bois 
Reymond  was  carrying  on  those  researches  into 
animal  electricity  that  have  made  him  famous. 
Helmholtz  witnessed  and  took  part  in  many  of  his 
experiments,  favoured  him  with  criticisms,  and  solved 
theoretical  problems  that  arose  in  the  course  of 
the  enquiry,  more  especially  as  to  the  distribution 
of  electricity  on  conductors  of  various  forms.  By 
using  a  delicate,  high-resistance  galvanometer,  and 
by  the  use  of  non-polarizable  electrodes,  a  new 
impulse  was  given  to  the  experimental  investigation 
of  animal  electricity.  If  from  living  muscle,  for 
example,  currents  could  be  led  off  into  the  gal- 
vanometer, as  had  been  done  by  Nobili  about  1827 
and  by  Matteucci  ten  years  later,  it  was  manifestly 
104 


HELMHOLTZ  IN  KONIGSBERG 

of  great  importance  that  no  contact  or  galvanic 
electricity  should  be  generated  by  bringing  the 
electrodes  against  the  living  tissue.  The  desideratum 
was  what  is  now  called  a  system  of  non-polarizable 
electrodes.  Helmholtz  tried  unsuccessfully  to  make 
such  electrodes  of  pure  silver  immersed  in  a  solution 
of  a  salt  of  silver.  Later  it  was  found  that  pure 
zinc  amalgamated  on  the  surface,  and  immersed  in 
a  saturated  solution  of  sulphate  of  zinc  practically 
fulfilled  the  conditions,  a  result  that  could  not  have 
been  theoretically  anticipated,  and  was  discovered  by  a 
lucky  hit.  With  pads  of  blotting  paper  immersed 
in  zinc  troughs  containing  the  solution  of  sulphate 
of  zinc,  and  with  pads  of  sculptor's  clay  moistened 
with  saliva  laid  on  the  paper  pads  to  protect  the 
muscle  from  the  irritant  action  of  the  sulphate  of 
zinc,  perfect  non-polarizable  electrodes  were  obtained. 
It  was  then  demonstrated  that  if  a  living  muscle, 
say  the  gastrocnemius  of  a  frog,  is  cut  in  transverse 
section,  and  if  one  clay  point  is  applied  to  the  middle 
of  the  longitudinal  surface  and  the  other  to  the  middle 
of  the  transverse  section,  a  current  will  flow  through 
the  galvanometer  in  such  a  direction  as  to  indicate 
that  the  surface  is  positive  to  the  transverse  section. 
To  explain  these  phenomena,  Du  Bois  Reymond 
advanced  a  physical  theory  which  may  thus  be 
shortly  described.  If  we  take  a  cylinder  of  zinc, 
having  a  bit  of  copper  soldered  on  each  side,  and 
plunge  it  into  dilute  sulphuric  acid,  or  even  water, 
105 


HERMANN  VON  HELMHOLTZ 

there  are  formed  an  infinite  number  of  currents, 
which  travel  through  the  water  from  the  zinc  to  the 
copper,  and  a  portion  of  these  may  be  conveyed  by 
conductors  applied  to  the  zinc  and  to  the  copper. 
If,  then,  a  galvanometer  be  interposed  in  the  circuit,  it 
will  be  found  that  the  zinc,  forming  the  centre  of  the 
cylinder,  is  positive,  and  that  the  copper,  forming  the 
sides,  is  negative,  a  result  comparable  to  that  obtained 
from  a  muscle.  Du  Bois  Reymond  therefore  sug- 
gested that  each  muscular  fibre  is  composed  of  an 
infinite  number  of  small  electro-motive  elements, 
analogous  to  the  cylinder  composed  of  zinc  and 
copper  above  described.  Each  little  element  would 
have  a  positive  equatorial  zone  and  two  negative  polar 
zones,  and  we  may  conceive  it  to  be  plunged  into  an 
intermediate  conducting  material.  He  did  not  mean 
that  these  electromotive  molecules,  or  'carriers  of 
electromotive  force,'  existed  in  any  histological  sense  ; 
they  were  to  be  regarded  as  nothing  more  than 
'  the  foci  of  chemical  change,'  and  they  were  analo- 
gous to  the  molecules  entering  into  the  conception 
of  the  physicist  when  he  discusses  electrolysis. 

Du  Bois  Reymond,  in  his  earlier  experiments, 
thought  he  obtained  a  current  from  an  uninjured 
muscle,  that  is,  from  one  whose  longitudinal  and 
transverse  sections  were  natural  and  not  artificially 
produced.  Later,  however,  he  discovered  that  if 
special  precautions  had  been  taken  not  in  the  slightest 
degree  to  injure  the  muscle,  no  current  was  obtained 
1 06 


HELMHOLTZ  IN  KONIGSBERG 

in  the  resting  state,  though  on  the  production  of 
tetanus,  caused  by  irritating  the  nerve  supplying  the 
muscle,  a  negative  variation,  or  current  in  the  opposite 
direction,  was  observed.  If  a  current  were  obtained 
when  the  muscle  was  at  rest,  it  was  in  greatly 
diminished  amount,  and  might  even  be  in  a  con- 
trary direction.  This  was  explained  by  supposing 
that  in  the  uninjured  muscle,  the  tendonous  end, 
which  is  the  natural  transverse  section,  contains  a 
layer  of  electromotive  molecules,  with  their  poles 
reversed,  so  that  their  positive  surface  is  towards  the 
transverse  section.  This  layer  Du  Bois  Reymond 
termed  the  parelectrotonic  layer,  and  when  one 
removes  it  by  making  an  artificial  cross  section,  the 
full  muscle  current  is  obtained. 

The  laws  of  the  dispersion  of  currents  in  irregularly 
shaped  conductors  had  been  only  partially  determined 
for  conductors  of  two  dimensions  by  Kirchhoff,  and  for 
three  by  Smaasen,  but  the  results  were  not  sufficient 
for  the  complicated  conditions  of  a  muscle.  It  was 
also  difficult  to  show,  on  the  electromotive  molecule 
theory,  why  weak  currents  could  be  obtained  from 
a  point  say  in  the  centre  of  the  transverse  section  and 
any  other  point  in  the  transverse  section  near  the  peri- 
phery, and  also  between  a  point  in  the  equatorial  region 
of  the  muscle,  on  its  surface,  and  any  point  nearer  each 
end.  These  results  could  not  be  explained  by  the 
copper-zinc  model.  Helmholtz  stepped  in  here,  and, 
by  his  analytical  power,  developed  the  theory  of 
107 


HERMANN  VON  HELMHOLTZ 

current  distribution  in  non-prismatic  conductors. 
He  showed  that,  on  the  assumption  of  peripolar 
molecules  in  the  muscle  substance,  no  weak  currents 
could  occur  on  the  surface  or  in  transverse  sections, 
and  that  the  difference  of  potential  between  the 
surface  and  the  transverse  section  would  not  increase 
with  the  size  of  the  muscle.  He  also  showed  that 
the  differences  between  the  results  of  the  actual 
experiment  and  what  was  to  be  expected  from  Du 
Bois  Reymond's  assumption  might  simply  be  due  to 
the  weakening  of  the  electromotive  forces  by  contact 
with  air,  with  fluids  such  as  are  used  in  the  experiment, 
and  by  dying  of  the  muscle  substance.  Further,  he 
argued  that  the  electromotive  forces  in  the  muscle,  and 
certainly  in  the  model,  are  modified  by  polarization. 
Subsequent  experiments  by  Du  Bois  Reymond  him- 
self, and  especially  by  Hermann,  support  this  view. 

In  the  address  given  by  Donders,  when  he  presented 
Helmholtz  with  the  von  Graefe  medal,  he  said  that 
the  latter  had  denied  the  pre-existence  of  electro- 
motive forces  in  muscle.  This  observation  evidently 
caused  some  annoyance  to  Du  Bois  Reymond,  as,  in 
his  eloge  on  Helmholtz,  he  repudiates  the  statement. 
No  doubt,  in  one  of  his  writings,  Helmholtz  indicated 
that  in  the  uninjured  muscle  no  current  could  be 
demonstrated  between  the  surface  and  the  natural 
cross  section  (tendon),  but  he  explained  to  Du  Bois 
Reymond  that  this  was  a  mistake,  and  that  the  unin- 
jured natural  cross  section  was  either  weakly  negative 
108 


HELMHOLTZ  IN  KONIGSBERG 

or  neutral,  and  sometimes  even  weakly  positive  to  the 
longitudinal  surface.  Du  Bois  Reymond  further 
states  : — c  But  so  little  did  Helmholtz  intend  to  deny 
the  pre-existence  of  electrical  forces  in  muscle,  that, 
on  the  contrary,  in  the  paper  we  are  here  considering, 
he  allows  my  hypothesis  of  the  peripolar  electromotive 
molecules  full  play  as  the  cause  of  the  muscle  current, 
and  declares,  in  so  many  words,  "  it  stands  to  reason 
that  the  electric  forces  of  the  current-surrounded 
molecules  must  be  taken  into  account  in  any  theory 
of  their  movement."  '  Further,  Helmholtz  suggested 
a  theory  to  Du  Bois  Reymond  in  which  the  electro- 
motive effects  were  harmonised  with  the  phenomena 
of  muscular  contracility,  but  this  does  not  appear  to 
have  been  published. 

These  views  of  Du  Bois  Reymond,  which  had  at 
all  events  the  qualified  support  of  Helmholtz,  found  an 
opponent  in  Ludwig  Hermann,  then  professor  in 
Zurich,  and  now  in  the  chair  in  Konigsberg,  once 
occupied  by  Helmholtz.  He  demonstrated  that  in  the 
absolutely  uninjured  frog's  muscle  there  is  no  current, 
and  showed  conclusively,  that  the  current  of  the  rest- 
ing muscle,  when  it  is  cut  in  transverse  section,  as 
directed  by  Du  Bois  Reymond,  causes  the  death  of  a 
thin  layer  of  the  muscle,  and  so  produces  difference  of 
potential.  This  difference  theory  refers  all  electro- 
motive effects  of  muscle  to  two  kinds  of  physiological 
change.  The  first  part  of  the  theory  is,  that  the  dying 
portion  of  the  substance  behaves  itself  negatively  to 
109 


HERMANN  VON  HELMHOLTZ 

the  living,  and  the  electromotive  force  has  its  seat 
in  the  demarcation  zone  between  the  living  and  the 
dying.  To  this  he  adds  a  rider,  that  not  only  death, 
but  irritation  as  well,  causes  the  affected  substance  to 
become  negative  to  the  unaffected  portion.  He 
further  shows  that  the  really  important  electrical 
phenomenon  is  the  negative  variation,  that  is  the 
current  flowing  in  the  reverse  direction  when  the 
muscle  is  caused  to  contract,  now  called  the  action 
current.  Still  it  must  be  observed  that  Hermann's 
statement  is  no  final  explanation.  It  does  not  explain 
why  the  dying  muscle  becomes  negative  to  the  living, 
and  it  is  possible  that  again  we  may  be  obliged  to  have 
recourse  to  some  such  hypothesis  as  that  of  Du  Bois 
Reymond. 

Helmholtz,  when  he  was  showing  electrical  experi- 
ments of  this  nature  to  his  audience  of  students  at 
Konigsberg,  hit  upon  the  device  (not  original,  how- 
ever) of  attaching  a  bit  of  silvered  glass  to  the  astatic 
needle  of  his  galvanometer,  and  by  this  means  he 
reflected  a  beam  of  light  on  a  screen,  thus  making  it 
possible  to  see  at  a  distance  the  smallest  movement  of 
the  needle.  This  method  was  independently  employed 
for  the  galvanometer  and  electrometer  by  Thomson 
(now  Lord  Kelvin),  and  it  has  adaptations  well  known 
in  every  laboratory.  It  was  about  this  time  also 
that  he  perfected  the  arrangements  for  equalising  the 
opening  and  closing  shocks  of  the  induction  coil 
described  in  chapter  iv.,  p.  36. 
no 


HELMHOLTZ  IN  KONIGSBERG 

His  physiological  work  also  led  Helmholtz  to  in- 
vestigate the  phenomena  of  induction  currents,  more 
especially  as  to  their  duration.  He  also  studied  the 
physiological  effects,  observed  by  Briicke,  of  electric 
shocks  of  extremely  short  duration  in  large  conductors 
applied  to  the  human  body.  These  researches  led  to 
the  invention  of  the  well-known  pendulum  myograph. 

Du  Bois  Reymond  mentions  as  an  amusing  example 
of  Helmholtz's  untiring  energy  that,  as  a  recreation 
between  periods  of  intense  mental  activity,  he  was  in 
the  habit  of  watching  through  a  telescope  the  good 
people  of  Konigsberg  as  they  walked  along  the  streets 
near  his  laboratory.  Weber  had  studied  human  loco- 
motion, describing  and  drawing  the  movements  of 
the  limbs.  Helmholtz  found  that  Weber  had  made 
several  mistakes,  more  especially  as  to  the  way  of  put- 
ting down  the  foot,  and  his  observations  were  verified 
long  afterwards  by  instantaneous  photography  and  by 
other  methods  devised  by  Marey,1  Professor  of  Physi- 
ology at  the  College  of  France. 

1  E.  J.  Marey,  Animal  Mechanism,  Book  II.,  chap.  iii.     London,  1874. 


CHAPTER     X 

HELMHOLTZ    IN    KfiNIGSBERG STUDIES    IN    COLOUR 

FROM  1852  to  1856,  when  he  removed  to 
Bonn,  Helmholtz  was  much  occupied  with 
the  phenomena  of  colour.  Thus,  in  1852,  there 
appeared  the  paper  on  Sensation  already  alluded  to  ; 
two  papers,  the  first  mainly  critical,  and  the  second 
more  constructive,  on  Sir  David  Brewster's  Analysis 
of  Sunlight,  and  a  fundamental  paper  on  the  Theory 
of  Colour;  and  in  1855  we  have  three  papers,  all 
dealing  with  colour  sensation.  As  often  happens, 
the  minds  of  men  of  science  in  different  parts  of  the 
world  may  be  occupied  with  the  same  question  about 
the  same  period  of  time.  The  rifts  in  the  clouds 
through  which  shafts  of  sunlight  pass  down  to  the 
earth  may  be  observed  only  by  the  few,  but  here  and 
there,  in  the  crowd,  the  eyes  of  keen  observers  are 
attracted  by  their  beauty.  Just  about  this  time  the 
phenomena  of  colour  were  almost  simultaneously 
before  the  minds  of  Sir  David  Brewster,  James  Clerk 
Maxwell,  and  Helmholtz.  Brewster  was  first  in  the 
field,  his  paper  appearing  in  The  Transactions  of  the 
Royal  Society  of  Edinburgh  in  1822.  The  first  pub- 

112 


HELMHOLTZ  IN  KONIGSBERG 

lished  paper  of  Maxwell  was  a  letter  to  Dr  George 
Wilson,  to  be  found  in  the  Transactions  of  the  Royal 
Society  of  Arts  for  1855,  but  he  had  before  this  date 
been  experimenting  with  his  well-known  colour  top, 
and  the  results  of  his  experiments  are  recorded  in 
the  Transactions  of  the  Royal  Society  of  Edinburgh, 
vol.  xxi.,  p.  185.  As  already  mentioned,  in  1852, 
Helmholtz  published  his  first  paper. 

To  appreciate  the  work  of  these  distinguished 
men,  and  more  especially  the  part  taken  by  Helm- 
holtz in  placing  the  theory  of  colour  on  a  sound 
basis,  let  us  go  back  for  a  little  to  fundamental 
ideas  regarding  light,  gradually  accumulated  before 
they  appeared  on  the  scene.  It  was  once  held 
that  a  luminous  body  shoots  out  from  itself  minute 
particles,  which,  passing  to  the  observer's  eye,  give 
rise  upon  impact  to  the  sensation  of  light.  This 
corpuscular  theory,  while  it  satisfactorily  explained 
many  of  the  facts,  failed  in  an  explanation  of  others, 
and  it  has  now  been  entirely  disproved.  Its  place  is 
taken  by  the  undulatory  theory,  first  suggested  by 
Huygens  in  1690,  reconciled  to  some  extent  with  the 
discoveries  of  Newton  by  Euler,  advocated  by  Hartley, 
and  finally  established  by  a  study  of  the  phenomena  of 
interference  by  Thomas  Young  and  by  Fresnel.  This 
theory  gives  a  complete  explanation  of  all  the  pheno- 
mena of  light.  According  to  this  view,  light,  objec- 
tively considered,  is  simply  a  mode  of  motion  of  a 
substance  called  the  luminiferous  ether  which  pervades 
H 


HERMANN  VON  HELMHOLTZ 

not  only  what  is  commonly  regarded  as  space,  but 
also  all  translucent  substances.  By  the  molecular 
movements  of  luminous  bodies,  this  ether  is  set  vibrat- 
ing in  a  series  of  waves.  The  ether  vibrations  that 
constitute  these  waves  may  be  conceived  to  be  at 
right  angles  to  the  direction  of  the  ray  of  light,  just 
as  the  surface  of  calm  water,  which  has  been  agitated 
by  a  stone,  rises  and  falls  as  the  waves  spread  outwards. 
Thus  a  cork  floating  on  the  water,  traversed  by  a 
wave,  oscillates  up  and  down  nearly  at  right  angles  to 
the  direction  of  the  wave.  These  wave-like  move- 
ments of  the  ether  impinging  on  the  retina  set  up  in  it 
changes  which  result,  after  their  effect  has  been  trans- 
mitted to  the  brain,  in  the  sensation  of  light,  but  the 
sensation  in  no  way  resembles  its  physical  cause, 
although  it  varies  with  variation  of  the  stimulus.1 
The  intensity  of  the  sensation  varies  with  the  ampli- 
tude of  the  wave.  Large  waves  give  rise  to  a  sensa- 
tion of  bright  light,  small  waves  to  a  sensation  of  dim 
light.  Again,  the  sensation  of  colour  depends  on  the 
rapidity  with  which  the  waves  follow  one  another,  or, 
in  other  words,  on  the  length  of  the  wave.  This 
rapidity,  though  inconceivably  great,  may  still  be 
accurately  determined.  Ordinary  sunlight,  as  Newton 
showed,  is  composed  of  a  series  of  colours  (using  the 
word  in  an  objective  sense)  blended  together,  but  yet 
separable  from  one  another,  because  each  colour  is  due 

1  Physiology  of  the  Senses.      By  M'Kendrick  and  Snodgrass.     London. 
1893,  p.   115. 

114 


HELMHOLTZ  IN  KONIGSBERG 

to  a  series  of  waves  differing  in  rate  of  succession  from 
the  others.  Thus  the  waves  that  give  rise  to  a  sensa- 
tion of  red  light  follow  each  other  at  the  rate  of  about 
435  millions  of  millions  per  second,  while  those  of 
violet  light  succeed  each  other  at  about  764  millions 
of  millions  per  second.  Between  these  we  have  an 
infinite  number  of  series  of  waves,  each  giving  rise 
to  a  special  colour  sensation,  and  so  between  the  red 
and  the  violet  of  the  spectrum  we  have  a  gradation  of 
colour  roughly  described  as  orange,  green,  blue  and 
indigo,  but  each  of  these  is  itself  made  up  of  countless 
shades,  which  melt  as  gradually  and  imperceptibly 
into  one  another  as  the  colours  of  a  sunset  sky.  The 
retina  is  not  sensitive  to  vibrations  of  the  ether  suc- 
ceeding each  other  more  slowly  than  those  of  red 
light,  although  it  may  be  demonstrated  that  these 
exist  and  originate  electrical  and  thermal  phenomena  ; 
nor  to  those  which  come  more  quickly,  although  the 
latter  have  marked  chemical  activity,  and  give  rise 
to  fluorescence. 

Solar  or  white  light  is,  then,  a  compound  of  all  the 
colours  in  definite  proportion.  A  body  which  reflects 
solar  light  to  the  eye  without  changing  this  propor- 
tion appears  to  be  white  ;  but  if  it  absorbs  all  the 
light,  so  as  to  reflect  no  light  to  the  eye,  it  appears  to 
be  black.  If  a  body  held  between  the  eye  and  the 
sun  transmits  light  unchanged  and  is  transparent,  it 
is  colourless  ;  but  if  translucent,  it  is  white.  If  it 
transmits  or  reflects  some  rays  and  absorbs  others,  it 


HERMANN  VON  HELMHOLTZ 

is  coloured.  If,  for  example,  it  absorbs  all  the  rays  of 
the  solar  spectrum  but  those  which  give  rise  to  the 
sensation  of  greenness,  we  say  that  the  body  is  green 
in  colour.  But  this  greenness  can  only  be  perceived 
if  the  rays  of  light  falling  on  the  body  contain  rays 
which  have  the  special  vibratory  rate  that  is  required 
for  this  special  colour.  For,  if  we  use  as  our  light 
any  other  pure-coloured  ray  of  the  spectrum,  say  the 
red,  its  rays  being  absorbed,  the  body  appears  to  us  to 
be  black.  A  white  surface  seen  in  a  red  light  seems  to 
be  red,  in  a  green  light  green,  as  it  reflects  all  colours 
alike,  absorbing  none.  To  the  normal  eye  the  colour 
physically  depends,  then,  on  the  nature  of  the  surface 
of  the  body,  as  was  first  shown  by  Robert  Boyle, 
and  of  the  light  falling  upon  it,  and  the  sensation  of 
colour  only  arises  when  the  body  reflects  or  transmits 
the  special  rays  to  the  eye.  If  two  rays  of  different 
wave-lengths  affect  one  part  of  the  retina  at  the  same 
time,  they  are  fused  together,  and  we  have  the  sensa- 
tion of  a  third  colour  different  from  its  cause.  Thus, 
if  red  be  removed  from  the  solar  spectrum,  all  the 
others  combined  will  give  a  sensation  of  a  greenish 
yellow,  although  we  cannot,  with  the  unaided  eye, 
analyse  this  into  its  components.  Certain  colour 
sensations,  such  as  red  or  green,  are  simple  in  the 
sense  that  they  cannot  be  originated  by  any  combina- 
tions of  other  colours  ;  while  other  colours,  such  as 
purple,  can  be  produced  by  certain  definite  mixtures, 
and  they  are  therefore  called  compound. 
116 


HELMHOLTZ  IN  KONIGSBERG 

Newton  laid  the  foundation  of  the  theory  of  com — 
pound  colours.  He  showed  that  two  beams  that  differ 
optically,  that  is  as  regards  the  periods  and  amplitudes 
of  their  ether  vibrations,  may  be  alike  chromatically, 
that  is  to  say,  they  may  give  rise  to  the  same  kind  of 
colour  sensation.  Thus,  by  mixing  red  and  yellow, 
an  orange  colour  may  be  produced  like  that  of  the 
spectrum,  but  differing  from  it  in  that  the  former  may 
still  be  analysed  by  a  prism  into  red  and  yellow,  whereas 
the  orange  of  the  spectrum  cannot  be  so  resolved. 
By  his  well-known  diagram  of  colour,  Newton  also 
showed  that  in  any  mixture  of  colours,  the  quantity 
and  quality  of  each  being  given,  it  was  possible  to 
determine  the  colour  of  the  compound.  While  the 
result  of  mixture  of  colours  in  the  production  of 
compounds  can  thus,  by  a  geometrical  method,  be 
represented  with  approximate  correctness,  their  true 
relations,  as  was  shown  by  Clerk  Maxwell,1  can  only 
be  determined  by  direct  experiment. 

With  his  usual  experimental  dexterity  and  philoso- 
phical acumen,  Thomas  Young  was  led  to  a  great 
generalisation  on  the  subject  of  colours,  in  which  it  is 
asserted  that  the  three  simple  colour  sensations  are 
red,  green  and  violet,  and  while  these  cannot  be 
produced  except  by  the  impact  of  light  of  a  certain 
wave-length  on  the  retina,  and  are  therefore  simple, 
any  other  colour  may  be  matched  by  a  mixture  of 

1  An  interesting  account  of  Clerk  Maxwell's  work  on  the  subject  is 
given  by  Glazebrook  in  his  Life  of  Max-well.  London,  1896,  p.  93. 


HERMANN  VON  HELMHOLTZ 

these  three  primaries.  The  quality  of  the  compound 
colour  so  produced  depends  on  the  proportion  of  the 
intensities  of  the  components,  and  its  brightness 
depends  on  the  sum  of  these  intensities.  There  is  no 
proof  that  these  effects  depend  entirely  on  changes 
occurring  in  the  retina ;  the  probability  is,  as  was 
indeed  suggested  by  Young  himself,  that  they  are 
connected  with  phenomena  occurring  in  the  brain. 

Sir  David  Brewster l  developed  a  new  theory  of 
colour  sensation,  in  which  the  three  primitive  colours 
were  red,  yellow  and  blue,2  and  it  was  assumed  that 
they  corresponded  to  three  kinds  of  objective  light. 
Each  of  these  varieties  gave  throughout  the  spectrum 
rays  of  all  degrees  of  refrangibility,  but  the  red  pre- 
dominated at  the  lower  end,  blue  at  the  upper  end, 
while  yellow  ruled  the  middle.  Coloured  media 
absorbed  in  different  proportions  rays  of  the  same  re- 
frangibility, but  of  different  colours.  This  theory  was 
combated  by  Airy,  Draper  and  Melloni,  and  it  has 
now  been  entirely  abandoned.  It  was  founded  mainly 
on  the  colours  apparently  assumed  by  light  in  passing 
through  various  transparent  and  colourless  media ; 
phenomena,  however,  that  can  be  explained  by  disper- 
sion or  diffusion  even  in  clear  prisms  and  in  the  media 
of  the  eye.  Brewster's  investigations  undoubtedly 
led  to  renewed  research,  and  it  was  at  this  point 

1  Trans,  of  Royal  Soc.  of  Edinburgh,  ix.,  p.  433  ;  xii.,  p.  123.     Pogg. 
Annalen,  xxiii.,  p.  435. 

2  Leonardo  da  Vinci,  Trattato  della  pittura,  Paris,  1651,  named  four 
simple  colours,  yellow,  green,  blue  and  red. 

118 


HELMHOLTZ  IN  KONIGSBERG 

Helmholtz  took  up  the  subject.  We  have  it  on  his 
own  authority,  that  his  attention  was  directed  to  it  by 
a  consideration  of  Miiller's  doctrine  of  the  specific 
energy  of  nerves,  mentioned  at  p.  13.  In  his  speech 
on  receiving  the  Graefe  medal,  he  said,  '  Not  being 
inclined  to  describe  in  my  lectures  things  I  had  not 
myself  seen,  I  made  experiments  in  which  I  blended 
the  colours  of  the  spectrum  in  pairs.  To  my  aston- 
ishment, I  found  that  yellow  and  blue  gave  not  green, 
as  was  then  supposed,  but  white.  Yellow  and  blue 
pigments,  when  mixed,  no  doubt  gave  green,  and 
until  then  the  mixing  of  pigments  was  supposed  to 
produce  the  same  effect  as  the  mixing  of  the  colours 
of  the  spectrum.  This  observation  not  only  at  once 
produced  an  important  change  in  all  the  ordinarily  ac- 
cepted notions  of  colour  mixture,  but  it  also  had  an  even 
more  important  effect  on  my  views.  Two  master  minds 
of  the  first  rank,  Goethe  and  David  Brewster,  were  of 
opinion  that  yellow  and  blue  could  be  directly  seen  in 
green.  Their  observations  were  made  with  pigments, 
and  they  thought  they  could  divide  their  perception 
of  the  resulting  colour  into  two  parts,  yellow  and 
blue,  while  in  reality,  as  I  was  able  to  show,  neither 
were  present.  I  was  thus  drawn  over  to  the  em- 
pirical theory  of  perception,  and  it  indicates  even  now 
the  contrast  between  my  position  in  the  theory  of 
colour  perception  and  that  of  Hering  and  his  followers, 
who  hold  firmly  to  the  opinion,  that  one  can  decom- 
pose the  perception  into  its  component  parts.' 
119 


HERMANN  VON  HELMHOLTZ 

The  true  explanation  of  why  yellow  and  blue 
pigments  yield  green  may  thus  be  shortly  stated,  and 
almost  in  the  words  of  Helmholtz  : l — When  light 
falls  on  a  powder  composed  of  transparent  particles, 
only  a  small  portion  is  reflected  from  the  surface  ;  the 
rest  penetrates  the  particles,  and  is  only  returned  by 
the  surfaces  of  separation  of  particles  situated  more 
deeply.  Thus  a  single  plate  of  clear  glass  reflects 
•o^th  of  the  light  which  strikes  its  surface,  two  plates 
will  reflect  ^th,  and  many  plates  will  reflect  nearly 
the  whole  of  it.  If  the  glass  reflects  only  ^7th  of 
the  incident  light,  the  rest  must  be  reflected  by  the 
deeper  layer.  In  the  same  way  the  surface  of  coloured 
powders  furnishes  only  a  small  part  of  the  light  which 
emerges  from  them  ;  the  deeper  parts  give  back  a 
greater  proportion.  Light  reflected  from  the  surface 
is  always  white  ;  that  alone  which  is  returned  by  the 
deeper  layers  is  coloured  by  absorption,  and  the  tint 
will  be  deeper  as  the  light  penetrates  more  deeply. 
Consequently  coloured  powders  are  more  deeply 
coloured  if  the  grains  are  of  considerable  size  than  if 
they  are  very  minute.  Reflection  depends  on  the 
number  of  surfaces,  and  not  on  the  thickness  of  the 
particles.  Consequently,  if  the  particles  are  large,  the 
light  must  go  through  a  greater  thickness  to  reach  the 
same  number  of  reflecting  surfaces  than  if  the  particles 
are  small,  and  thus,  if  the  particles  in  a  thick  powder 
are  large,  the  rays  absorbable  by  the  substance  will  be 

1  Optiyue  Physiologique.     Paris,  1867,  p.  363. 
120 


HELMHOLTZ  IN  KONIGSBERG 

taken  up  to  a  greater  extent,  and  the  coloured  light 
coming  back  from  the  powder  will  be  deeper  and 
more  saturated  than  if  the  particles  were  small.  Sup- 
pose, now,  that  yellow  chrome  is  mixed  with  indigo 
blue.  The  light  reflected  from  the  particles  of  chrome 
will  be  orange,  yellow  and  green,  the  blue  and  violet 
being  absorbed,  and  that  from  the  indigo  blue  will  be 
green,  blue  and  violet,  the  orange  and  yellow  being 
absorbed.  If,  now,  the  light  that  has  passed  through 
a  particle  of  chrome  traverses  a  particle  of  indigo  blue, 
all  the  colours  will  be  absorbed  except  the  green. 
Consequently  the  green  alone  will  reach  the  eye. 

On  the  other  hand,  if  the  pure  spectral  colours, 
yellow  and  blue,  pass  into  the  eye  so  as  to  affect  the 
same  spot  on  the  retina,  the  result  is  a  sensation  of 
white,  because,  in  this  case,  both  the  yellow  and  the 
blue  wave-lengths  fall  on  the  terminal  organ.  This 
ingenious  explanation  has  many  important  applica- 
tions, not  only  as  regards  the  colours  .reflected  from 
mixtures  of  powders,  but  also  the  mode  of  action  of 
all  coloured  surfaces  both  in  the  inorganic  world  and 
on  the  surfaces  of  plants  and  animals.  It  shows  how 
the  texture  of  the  surface  modifies  the  result. 

Helmholtz  then  devised  an  ingenious  method  by 
which  two  spectra  could  be  simultaneously  examined, 
through  a  slit  shaped  like  the  letter  V,  in  such  a  way 
that  a  portion  of  one  spectrum  was  superposed  on  the 
other.  In  this  way  all  possible  mixtures  of  two 
simple  colours  could  be  made  with  the  intensities  of 
121 


HERMANN  VON  HELMHOLTZ 

the  colours  in  the  two  spectra,  and  the  mixed  rays, 
passing  through  a  lens,  were  directed  on  the  same 
spot  of  the  observer's  retina.  This  method  differs 
from  that  of  using  a  rotating  disc,  sectors  of  which 
could  be  coloured  at  pleasure,  a  method  used  by 
Thomas  Young,  but  worked  out  with  great  exacti- 
tude by  Clerk  Maxwell,  in  the  form  of  his  well-known 
colour  top.  The  arrangement  of  the  rotating  disc  is 
such  that  a  little  area  of  retina  is  struck  in  rapid 
succession  with  reflected  rays  of  different  wave- 
lengths, say  now  the  long  waves  of  red,  then  the 
short  of  violet,  with  the  result  that  the  sensation  is 
that  of  purple. 

By  mixing  the  pure  colours  of  the  spectrum,  Helm- 
holtz  showed  that  red  and  violet  gave  purple  ;  red 
and  blue,  rose  ;  red  and  green,  dull  yellow  ;  red  and 
yellow,  orange  ;  yellow  and  violet,  rose  ;  yellow  and 
and  blue,  white ;  yellow  and  green,  yellow-green  ; 
green  and  violet,  pale  blue ;  green  and  blue,  blue- 
green  ;  and  blue  and  violet,  indigo  ;  but  he  was  un- 
able by  any  combination  to  produce  red,  green  and 
violet.  Further,  he  formulated  several  important 
principles  with  regard  to  sensations  of  colour.  Thus 
the  quality  of  every  luminous  sensation  depends  on 
three  variables — luminous  intensity,  tone,  and  degree 
of  saturation.  A  sensation  of  colour  produced  by  a 
certain  quantity,  *,  of  coloured  rays  mixed  in  any  way 
whatever  may  be  always  reproduced  by  a  certain 
amount,  #,  of  white  light  with  a  certain  quantity,  />, 
122 


HELMHOLTZ  IN  KONIGSBERG 

of  a  saturated  spectral  colour  (or  purple)  of  a  deter- 
minate tone.  From  the  physical  point  of  view,  mixed 
light  is  compounded  of  various  waves  of  different  wave- 
lengths ;  but  the  sensation  caused  by  the  mixture  falling 
on  the  retina  may  be  always  considered  as  a  function  of 
three  variable  quantities — (i)  the  quantity  of  saturated 
coloured  light ;  (2)  the  quantity  of  white  light  which 
may  be  added  to  produce  the  same  sensation  of 
colour;  and  (3)  the  length  of  the  wave  of  coloured 
light.  He  also  investigated  mathematically  the  con- 
struction of  a  geometrical  table  of  colours.  Finally, 
he  revived  and  extended  the  hypothesis  of  Thomas 
Young,1  which  attempted  to  explain  and  account  for 
the  phenomena  of  colour. 

How  comes  it  that  we  perceive  differences  in 
colour  ?  \Ve  may  look  for  the  cause  in  various 
directions.  We  might  suppose  a  molecular  vibration 
to  be  set  up  in  the  nerve-endings  synchronous  with 
the  undulations  of  the  luminiferous  ether,  without 
any  change  in  the  chemical  constitution  of  the  sensory 
surface ;  and  we  might  suppose  that  where  various 
series  of  waves  corresponding  to  different  colours 
act  together,  these  are  fused  together,  or  interfere 
with  each  other  in  such  a  way  as  to  give  a  vibration 
of  modified  form  or  rate  corresponding  somehow  to 
the  sensation  arising  in  consciousness.  Or,  again, 
we  might  suppose  that  the  effect  of  different-coloured 
rays  is  to  promote  or  retard  chemical  changes  in  the 

1  Lectures  on  Natural  Philosophy,  1 807. 
I23 


HERMANN  VON  HELMHOLTZ 

sensory  surface,  which  again  so  affect  the  sensory 
nerves  as  to  give  rise  to  differing  states  in  the  nerves 
and  nerve  centres  with  differing  concomitant  sensa- 
tions. The  first  line  of  thought  is  at  the  basis  of 
the  hypothesis  of  Thomas  Young.  He  supposed  that 
there  are  three  fundamental  colour  sensations — red, 
green  and  violet — by  the  combination  of  which  all 
other  colours  may  be  formed,  and  that  there  are  in 
the  retina  three  kinds  of  nerve  elements,  each  of 
which  is  specially  responsive  to  the  stimulus  of  colour 
of  one  wave-length,  and  much  less  so  to  the  others. 
If  a  pure  red  colour  alone  act  on  the  retina,  only  the 
corresponding  nerve  element  for  red  sensation  would 
be  excited,  and  so  with  green  and  violet.  But  suppose 
the  colour  to  be  mixed,  then  the  nerve  elements  will 
be  set  in  action  in  proportion  to  the  amount  of  con- 
stituent excitant  rays  in  the  colour.  Thus,  if  all  the 
nerve  elements  be  set  in  action,  we  shall  have  white 
light ;  if  that  corresponding  to  the  red  and  green,  the 
resultant  sensation  will  be  orange  or  yellow  ;  if  mainly 
the  green  and  violet,  the  sensation  will  be  blue  or 
indigo,  and  the  like.  Helmholtz  succinctly  puts  it  as 
follows  : — 

(i.)  Red  excites  strongly  the  fibres  sensitive  to 
red,  and  feebly  the  other  two — sensation, 
red. 

(2.)  Yellow  excites  moderately  the  fibres  sensitive 
to  red  and  green,  feebly  the  violet — sensa- 
tion, yellow. 

124 


HELMHOLTZ  IN  KONIGSBERG 

(3.)  Green  excites  strongly  the  green,  feebly  the 

other  two — sensation,  green. 

(4.)  Blue  excites  moderately  the  fibres  sensitive  to 
green  and  violet,  and  feebly  the  red — sen- 
sation, blue.  • 

(5.)  Violet  excites  strongly  the  fibres  sensitive  to 
violet,  and  feebly  the  other  two — sensation, 
violet. 

(6.)  When  the  excitation  is  nearly  equal  for  the 
three  kinds  of  fibres,  then  the  sensation  is 
white. 

Another  mode  of  expressing  the  theory  is  to  say 
that  each  primary  sensation  of  red,  green  and  violet 
is  excited  in  some  degree  by  almost  every  ray  of  the 
spectrum,  but  the  maxima  of  excitation  occur  at 
different  places,  while  the  strength  of  stimulation  in 
each  case  diminishes  in  both  directions  from  the 
maximum  point.  Thus  when  the  three  sensations 
are  equally  excited,  white  light  is  the  result ;  green 
is  caused  by  a  very  weak  violet  stimulation,  a  stronger 
red,  and  a  still  stronger  green  stimulation.  At  each 
end  of  the  spectrum  we  have  only  the  simple  sensa- 
tions of  red  and  violet,  and  all  the  intermediate  colour 
sensations  are  compounds  of  varying  proportions  of 
the  three  primaries. 

According  to  this  theory,  red  blindness  is  attribut- 
able to  the  absence  of  the  red  sensation,  and  green 
blindness   to    the   absence    of    the    green    sensation. 
When   the  green  and   violet  sensations  are  equal  in 
125 


HERMANN  VON  HELMHOLTZ 

amount,  a  red-blind  person  sees  what  is  to  him  white, 
and  when  the  red  and  violet  are  equal,  a  green-blind 
person  will  have  a  sensation  of  what  in  turn  is  to  him 
white,  although,  to  the  normal  eye,  these  parts  are 
bluish-green  in  the  one  case  and  green  in  the  other, 
as  the  green  sensation  is  in  each  added  to  the  sensa- 
tions of  red  and  blue. 

The  subject  is  fully  discussed  in  Helmholtz's  great 
work,  Handbuch  der  physiologischen  Optik,  the  first  part 
of  which  appeared  in  1856  and  the  last  in  1867.  The 
first  part  of  a  new  edition  appeared  in  1885,  and  the 
last  in  the  year  of  the  death  of  Helmholtz,  1894.  In 
the  new  edition  he  returns  to  the  subject  of  colour 
vision,  and  materially  modifies  the  views  in  his  earlier 
writings  as  to  what  is  now  universally  known  as  the 
Young-Helmholtz  theory  of  colour  sensation.  It  is 
fitting  that  the  two  great  names  should  be  linked 
together.  Helmholtz  finally  held  that  luminosity  or 
brightness  plays  a  more  important  part  in  our  per- 
ceptions of  colour  than  has  been  supposed.  He  also, 
by  analysing  the  colours  of  the  spectrum  with  great 
care,  aided  by  his  pupils,  and  more  especially  by 
Arthur  Konig,  was  able  from  these  data  to  determine 
three  fundamental  colour  sensations,  the  first  red  (a), 
which  is  a  highly-saturated  carmine-red  ;  the  second 
green  (/>),  like  the  green  of  vegetation  ;  and  the  third 
blue  (c),  like  ultra-marine.  Each  spectral  colour  he 
supposed  to  be  made  up  of  certain  proportions  of  these 
fundamental  colours,  or  of  a  combination  of  two  of 
126 


HELMHOLTZ  IN  KONIGSBERG 

them  added  to  a  certain  amount  of  white.  Thus 
100  parts  of  green  are  composed  of  15  of  #,  51  of  />, 
and  34  of  c ;  or,  to  take  other  examples,  spectral  red 
contains,  in  100  parts,  42  of  #,  I  of  £,  and  57  of  white  ; 
yellow — ii  of  a,  14  of  £,  and  75  of  white  ;  and  blue 
— 2  of  a,  ii  of  f,  and  87  of  white.  The  white  gives 
the  element  of  brightness.  According  to  this  view, 
it  is  not  necessary  to  suppose  that  in  the  red- 
blind  the  red-perceiving  elements  are  awanting,  or 
that  in  the  green-blind  the  green-perceiving  elements 
are  absent,  but  that  these  elements  may  be  stimulated 
with  intensities  different  from  those  affecting  the 
normal  eye.1 

It  is  foreign  to  the  purpose  of  this  book  to  criticise 
the  theory,  or  to  contrast  it  with  the  rival  theory  of 
Hering,  which  assumes  molecular  processes  in  the 
retina  of  a  katabolic  (pulling  down  or  disintegrative) 
and  an  anabolic  (building  up  or  reconstructive)  kind. 
Suffice  it  to  say,  that  while  there  are  a  few  special 
cases  not  yet  completely  explained  by  the  Young- 
Helmholtz  theory,  on  the  whole  it  accounts  for 
the  general  facts  in  a  satisfactory  and  convincing 
manner. 

The  investigation  is  eminently  characteristic  of 
Helmholtz.  He  examined  the  facts  with  the  min- 
utest care,  and  with  the  aid  of  arrangements  and 
apparatus  of  the  most  ingenious  and  perfect  kind,  and 
then  he  endeavoured  to  refer  all  the  facts  to  a  general 

1  M'Kendrick  and  Snodgrass,  of.  cit.,  p.  169. 
I27 


HERMANN  VON  HELMHOLTZ 

principle.  As  remarked  by  Sir  John  Herschel,1  '  we 
must  never  forget  that  it  is  principles,  not  phenomena 
— laws,  not  insulated  independent  facts — which  are  the 
objects  of  inquiry  to  the  natural  philosopher.  As 
truth  is  simple,  and  consistent  with  itself,  a  principle 
may  be  as  completely  and  as  plainly  elucidated  by  the 
most  familiar  and  simple  fact,  as  by  the  most  imposing 
and  uncommon  phenomenon.  The  colours  which 
glitter  on  a  soap-bubble  are  the  immediate  conse- 
quences of  a  principle  the  most  important  from  the 
variety  of  phenomena  it  explains,  and  the  most 
beautiful,  from  its  simplicity  and  compenduous  neat- 
ness, in  the  whole  science  of  optics.' 

1  Discourse  on  the  Study  of  Natural  Philosophy.     London,  1830,  p.  13. 


128 


CHAPTER    XI 

HELMHOLTZ    IN    BONN    AND    HEIDELBERG 

SENSATIONS   OF    TONE 

HELMHOLTZ  was  appointed  to  be  Professor 
of  Physiology  at  Bonn  in  1856,  when  he  was 
thirty-five  years  of  age,  and  near  the  zenith  of  his 
powers.  Here  he  remained  till  1859,  wnen  he  was 
invited  to  the  chair  in  Heidelberg,  a  position  he  filled 
till  1871.  The  three  years  at  Bonn  were  charac- 
terised by  the  same  intellectual  activity.  Having  in 
Konigsberg  laid  the  foundation  of  his  great  work  on 
physiological  optics,  he  next  proceeded  to  the  ex- 
amination of  the  sense  of  hearing,  and  here  he 
conquered  a  new  world,  and  made  it  peculiarly 
his  own.  Again,  the  guiding  principle  was  Johannes 
Miiller's  doctrine  of  specific  energy,  and  again  he 
proceeded  step  by  step  to  survey  the  whole  region 
of  inquiry — on  this  occasion  it  was  acoustics — from 
the  point  of  view  of  the  physiologist,  but  fully 
equipped,  not  only  with  anatomical  knowledge,  but 
with  all  the  methods  and  modes  of  reasoning  of  the 
mathematician  and  physicist. 


HERMANN  VON  HELMHOLTZ 

There  can  be  no  doubt  that  one  of  the  secrets  of 
the  marvellous  activity  in  research  of  Helmholtz  was, 
that  there  was  the  most  intimate  connection  between 
his  function  of  a  professor,  whose  duty  it  was  to 
teach,  and  that  of  an  original  investigator.  Teaching 
and  investigation  went  hand  in  hand.  He  investi- 
gated because  he  wished  to  speak  of  matters  at  first 
hand,  and  thus  he  did  not  merely  recapitulate  the 
views  of  others.  Again  and  again  he  took  up  a 
problem,  so  that  he  might  master  it  himself,  and  be 
enabled  to  make  it  clear  to  his  pupils.  Thus  there 
was  not  only  freshness  in  his  teaching,  as  he  was 
continually  breaking  new  ground,  but  he  was  year 
by  year  adding  to  scientific  knowledge.  It  is,  of 
course,  in  the  highest  degree  unlikely  that  the  im- 
petuous and  masterful  intellect  of  Helmholtz  would 
have  acted  otherwise  under  almost  any  circumstances  ; 
but,  at  the  same  time,  the  circumstances  in  which 
he  was  placed  favoured  its  development.  He  was 
obliged,  year  after  year,  to  take  a  general  survey  of 
his  science  ;  he  was  always  associated  with  the  young, 
and  there  is  nothing  more  inspiring  for  a  teacher 
than  to  have  to  satisfy  young  and  ardent  minds. 
Even  if  these  are  only  the  minority  of  a  class,  their 
presence  is  a  subtle  inspiration,  stimulating  to  new 
effort.  The  example  of  Helmholtz,  therefore,  is  a 
strong  argument  in  favour  of  combining  teaching 
with  working  ;  and  the  results,  not  only  in  his  case, 
but  in  many  others,  show  that,  in  the  advancement 
130 


HELMHOLTZ  IN  BONN 

of  science,  it  may  not  be  the  wisest  course  to  endow 
research  alone  and  to  relegate  the  researcher  to  a 
kind  of  monastic  solitude.  It  will,  on  the  whole,  be 
better  for  him  and  better  for  science  to  prosecute 
research,  because  he  must  communicate  to  others 
the  fruits  of  his  own  labours. 

The  first  paper  on  Physiological  Acoustics  ap- 
peared in  1854,  anc^  consisted  mainly  of  a  review  of 
the  work  done  by  others  up  to  1849.  The  ground 
having  in  this  way  been  cleared,  three  papers  appeared 
on  Combination  Tones  in  1856,  one  upon  Vowel  Tones 
in  1857,  a  lecture  on  the  Physical  Basis  of  Harmony 
and  Dissonance  in  1858,  another  on  Vowel  Tones, 
and  two  on  the  Theory  of  Open  Organ  Pipes  in 
1859,  a  PaPer  on  Musical  Temperature,  another  on 
the  Motions  of  the  Strings  of  a  Violin,  and  a  lecture 
on  Timbre  (Klangfarbe)  in  1860,  a  paper  on  Reed 
or  Tongued  Organ  Pipes  in  1861,  a  short  paper  in 
1862  on  the  Arabic  and  Persian  Scales,  and  at  last, 
in  1863,  there  appeared  the  great  work,  Die  Lehre 
von  den  Tonempfindungen  ah  physiologische  Grundlage  fur 
die  Theorie  der  Musik^  or  Sensations  of  Tone  as  the 
Physiological  Basis  of  Music.  A  well-known  mono- 
graph on  the  mechanics  of  the  bones  of  the  middle 
ear  and  of  the  drumhead  (membrana  tympani\  involv- 
ing an  elaborate  anatomical  investigation  of  these 
organs,  did  not  appear  till  1869. 

It  is  difficult  to  give  the  reader  an  adequate  notion 
either  of  the  work  on  physiological  optics  or  of  that  on 


HERMANN  VON  HELMHOLTZ 

physiological  acoustics.  They  must  be  read,  referred 
to,  consulted  over  and  over  again,  before  one  can 
appreciate  the  wealth  of  material  to  be  found  in 
these  volumes.  They  are  not  merely  historical 
accounts  of  all  that  has  been  done  up  to  the  date 
of  their  appearance  in  that  particular  department 
of  science,  but,  at  the  same  time,  the  bibliography 
is  of  the  most  complete  description,  showing  the 
unwearied  literary  activity  of  the  author.  A  notice 
is  given,  often  critical,  of  the  works  of  writers  from 
the  earliest  down  to  the  most  recent  times.  In 
these  notices  there  is  a  generous  estimate  of  the 
labours  of  those  who  have  gone  before.  There  is 
an  absence  of  polemical  writing ;  if  the  author  does 
not  agree  with  the  results  obtained  in  a  particular 
research,  this  is  frankly  stated,  and  the  experimental 
error,  or  the  illogical  result,  is  pointed  out  and  calmly 
brushed  aside.  But  great  as  are  the  merits  of  these 
books,  even  from  this  point  of  view,  their  charm  is 
their  freshness.  The  reader  feels  that  the  author  has 
gone  over  every  bit  of  the  ground  himself,  and  there 
is  scarcely  a  page  that  is  not  enlivened  by  the  results 
of  personal  research.  Everywhere  one  feels  the  grasp 
of  a  master,  whether  in  the  exposition  of  the  subject 
in  hand  or  in  its  mathematical  treatment ;  and  it  is 
characteristic  of  Helmholtz  that,  with  a  kind  of 
literary  modesty,  a  profound  mathematical  discussion 
of  a  difficult  question  is  often  relegated  to  an  appendix 
at  the  end  of  the  chapter,  whilst  it  really  may  con- 
132 


HELMHOLTZ  IN  BONN 

tain  not  only  the  gist  of  the  matter,  but  be  full  of 
suggestions  for  coming  observers. 

We  shall  now  endeavour  to  give  a  short  account 
of  the  contributions  of  Helmholtz  to  the  theory  of 
hearing,  and  in  doing  so  it  will  be  more  convenient 
and  intelligible  if  we  make  the  attempt,  not  in  the 
chronological  order  of  Helmholtz's  papers,  but  in 
connection  with  the  physiological  mechanism  of  the 
ear  itself.  Sound  waves  are  collected  by  the  external 
ear  and  transmitted  by  the  external  canal  or  meatus 
to  the  drumhead.  The  drumhead  is  subjected  to 
periodic  pressures  corresponding  to  the  individual 
waves  of  sound,  and  thus  it  moves  inwards  with  each 
pressure  and  outwards  by  its  elasticity.  These  move- 
ments of  the  drumhead  are  transmitted  across  the 
middle  ear  or  tympanum  to  the  internal  ear  by  a  chain 
of  bones,  the  malleus,  incus  and  stapes.  Lastly,  the 
internal  ear  consists  of  a  very  complicated  arrange- 
ment of  sacs,  in  which  lie  the  nerve  endings  immersed 
in  fluid,  and  the  nerve  endings  receive,  in  their  turn, 
the  pressures  communicated  by  the  chain  of  bones, 
ending  in  the  base  of  the  stapes,  which  fits  into 
the  oval  window.  How  these  nerve  endings  are  so 
affected  by  these  pressures  as  to  stimulate  the  fibres 
of  the  auditory  nerve  is  the  ultimate  problem  of 
hearing.  How  do  we  become  conscious  of  pitch, 
of  loudness  or  intensity,  and  especially  of  the  timbre, 
quality  or  klangfarbe  of  a  tone,  so  that  we  at  once 
recognise  the  instrument  producing  it,  whether  it  be 
133 


HERMANN  VON  HELMHOLTZ 

a  trumpet,  a  violin  or  a  human  voice  ?  It  will  be 
evident,  also,  that  an  answer  to  these  questions  con- 
stitutes what  Helmholtz  calls  the  physiological  basis 
of  sensations  of  tone.  The  answer,  however,  cannot 
explain  the  aesthetic  relations  of  music  ;  it  cannot 
explain  why,  of  all  the  arts,  this  is  the  one  which,  while 
it  is  the  most  intangible,  yet  stirs  the  very  depths  of 
our  being,  and  gives  expression  to  feelings,  longings, 
aspirations,  contemplations,  that  can  never  find  full 
recognition  in  the  most  splendid  efforts  of  the  painter 
or  the  sculptor.  The  work  of  Helmholtz,  in  the 
first  place,  laid  the  physiological  foundation,  and  after- 
wards he  did  little  more  than  indicate  the  path  along 
which  we  must  travel  from  the  foundation  into  the 
region  of  aesthetics.  Himself  a  musician,  not  only 
in  the  sense  of  enjoying  music,  but  also  because 
he  had  studied  theory  as  a  musician  is  obliged  to 
do,  and  because  he  was  thoroughly  acquainted  with 
musical  literature — and  especially  with  that  of  his 
great  countrymen  Beethoven,  Mendelssohn,  Wagner, 
and  the  brilliant  galaxy  of  lesser  German  composers — 
he  was  eminently  qualified  for  the  task.  Indeed,  it 
seemed  as  if  Nature  had  raised  in  Helmholtz  a  man 
of  such  a  rare  combination  of  endowments,  that  she 
could  safely  whisper  to  him  some  of  her  secrets  in 
this  borderland  of  physics,  physiological  action  and 
aesthetics,  feeling  assured  that  he  would  be  a  just  and 
faithful  interpreter. 

Helmholtz  was  the  first  to  examine  the  mechanism 


HELMHOLTZ  IN  BONN 

of  the  drumhead  in  a  satisfactory  manner.  Had  the 
drumhead  been  a  uniformly  flat-stretched  membrane, 
the  amplitude  of  its  movements,  in  response  to  the 
varying  pressures  of  sound  waves,  would  be  greatest 
in  the  centre,  while  it  would  diminish  as  the  periphery 
of  the  membrane  was  approached.  Helmholtz  showed 
that  it  is  not  flat,  but  composed  of  numerous  fibres  so 
arranged  as  to  present  the  convexity  of  a  curve  out- 
wards, that  is,  meeting  the  sound  waves  falling  upon 
them,  while  the  membrane,  as  a  whole,  bulges  in- 
wards. In  this  way  a  very  small  change  in  the 
pressure  of  the  air  causes  a  considerable  increase  in 
the  tension  of  the  fibres,  and  as  the  force  exerted 
upon  the  handle  of  the  malleus  (the  bone  attached 
to  the  membrane)  increases,  the  amplitude  of  the 
movement  of  that  bone  diminishes.  Thus  the  special 
form  of  the  drumhead  secures  a  maximum  of  efficiency 
for  tones  of  the  feeblest  intensity. 

He  then  proceeds  to  examine  the  mechanism  of  the 
chain  of  bones,  showing  that  they  constitute  a  lever 
in  which  the  force  is  applied  at  the  handle  of  the 
malleus  where  it  is  attached  to  the  membrane,  the 
fulcrum  where  the  short  process  of  the  incus  abuts 
against  the  wall  of  the  tympanum,  and  the  work  is 
done  at  the  base  of  the  stapes,  where  it  pushes  into 
the  oval  window,  on  the  other  side  of  which  we 
have  the  labyrinth.  The  lever  is  such  as  to  diminish 
the  amplitude  of  the  movements  at  the  base  of  the 
stapes,  while  the  work  is  done  over  a  smaller  area 
'35 


HERMANN  VON  HELMHOLTZ 

than  that  of  the  drumhead,  and  thus  effective,  but 
very  minute,  pushes  to  and  fro  are  communicated  to 
the  delicate  structures  in  the  inner  ear.  Helmholtz 
also  investigated  the  little  saddle-shaped  joint  between 
the  incus  and  the  head  of  the  malleus,  showing 
that  when  the  drumhead  was  pushed  in  very  strongly 
there  was  a  curious  rotation  of  the  surfaces  of  the 
bones  so  that  they  interlocked,  and  thus  further 
pressure  could  not  be  communicated  to  the  stapes  ; 
while,  on  the  other  hand,  if  the  drumhead  was 
distended  outwards,  as  by  inflating  the  tympanum 
through  the  Eustachian  tube,  there  was  no  danger  of 
pulling  the  base  of  the  stapes  out  of  its  place,  because 
the  little  joint  opened  up,  the  head  of  the  malleus 
swinging  free  from  the  depression  in  the  incus. 
Thus  the  danger  of  injuring  the  inner  ear  by  violent 
movements  of  the  drumhead,  either  outward  or 
inward,  is  reduced  to  a  minimum  by  these  exquisite 
arrangements.  In  this  investigation  Helmholtz  proves 
to  the  hilt  his  claim  to  be  a  competent  anatomist. 

It  was,  however,  in  the  region  of  the  internal  ear 
that  Helmholtz  won  for  physiological  science  the 
greatest  triumphs.  Up  to  the  date  of  his  investigations 
this  was  known  almost  solely  to  the  anatomists,  who 
laboriously  described  its  various  parts  and  covered  it 
over  with  a  barbarous  terminology,  which  is  still  the 
terror  of  students.  The  physiologists  had  little  to 
say  as  to  its  probable  functions,  and  the  mathe- 
maticians and  physicists  and  writers  on  acoustics 
136 


HELMHOLTZ  IN  BONN 

generally,  regarded  it  as  a  wilderness  of  sacs  and 
tubes  involving  problems  almost  incapable  of  solution.1 
Musicians,  on  the  other  hand,  did  not  expect  much 
help  from  physical  and  physiological  science.  Imbued 
with  a  love  of  their  art,  they  were  mainly  occupied 
with  the  consideration  of  its  aesthetic  relations,  they 
were  unacquainted  with  the  methods  of  scientific 
analysis,  and  they  rather  dreaded  investigations  into 
the  minute  structure  of  the  parts  and  also  the  tor- 
turing expedient  of  physical  experiment.  \Vhy  an 
octave  or  a  fifth  should  be  more  satisfying  to  the 
ear  than  a  minor  third  ;  why  certain  chords  had  a 
character  of  their  own  ;  what  was  the  physiological 
basis  of  discords  ;  what  was  the  true  nature  of  beats  ; 
what  was  the  physiological  significance  of  the  pro- 
gression of  the  notes  in  a  melody  ;  what  were  the 
physiological  laws,  if  any,  that  regulated  the  develop- 
ment of  musical  capacity  in  the  human  race ;  all 
these  were  questions  the  musicians  cared  little  about, 
and  if  they  did  allow  them  to  occupy  their  attention 
they  were  dismissed  as  insoluble.  Men  took  refuge 
in  the  notion  that  music  was  music  because  it  was 
adapted  to  our  spiritual  nature,  and  they  thought 
there  was  little  use  in  endeavouring  to  examine  the 
physical  and  physiological  materials  of  which  musical 
tones  were  composed.  Helmholtz  changed  all  this 
by  attempting  to  give  an  intelligible  account  of  the 
mechanism  of  the  internal  ear. 

1  Sir  G.  B.  Airy  on  Sound.     London,  1871. 

'37 


HERMANN  VON  HELMHOLTZ 

This  organ,  as  already  said,  consists  of  a  complicated 
series  of  sacs  and  tubes  filled  with  fluid.  In  certain 
situations  the  walls  of  the  sac  contain  highly-differen- 
tiated epithelial  structures,  which  are  intimately 
related  to  the  terminal  filaments  of  the  auditory 
nerve.1  The  problem  is  to  explain  how  the  pres- 
sures transmitted  by  the  foot  of  the  stapes  affect 
these  terminal  structures  in  such  a  way  as  to  excite 
sensations  corresponding  to  the  pitch,  intensity  and 
quality  of  tones. 

Two  small  sacs,  the  utricle  and  saccule,  are  the  first 
structures  that  receive  the  impulses  of  the  base  of  the 
stapes.  The  utricle  communicates  with  the  semi- 
circular canals,  and  the  saccule  with  the  long  spiral 
duct  of  the  cochlea.  The  oval  window,  into  which 
the  base  of  the  stapes  fits,  is  covered  by  a  membrane. 
Suppose  the  base  of  the  stapes  to  be  pushed  in  by  the 
pressure  of  a  wave  of  sound,  then,  since  the  delicate  sacs 
and  canals  are  all  inclosed  in  cavities  in  the  bone,  having 
rigid  walls,  it  is  clear  that,  as  the  fluid  is  practically 
incompressible  by  the  force  applied,  no  movements 
could  be  communicated  to  any  of  the  delicate  nerve- 
endings.  But  one  part  of  the  osseous  wall,  next  the 
tympanum  or  middle  ear,  has  a  round  opening,  also 
covered  by  a  membrane.  Thus,  when  the  base  of 
the  stapes  is  pushed  inwards,  the  membrane  cover- 

1  In  some  parts  of  this  chapter  I  make  free  use  of  an  article  on 
Hearing  in  Schafer's  advanced  Text-Book  of  Physiology,  vol.  ii.,  written  by 
my  pupil,  Dr  Albert  A.  Gray,  and  myself. 

138 


HELMHOLTZ  IN  BONN 

ing  the  round  window  passes  outwards,  and  thus  a 
to-and-fro  pressure  is  communicated  to  the  fluid 
in  the  sacs  and  tubes  with  each  pressure  of  a  wave 
of  sound. 

Helmholtz  emphasizes  strongly  a  remark  first  made 
by  Riemann,  that  the  dimensions  of  the  internal  ear  are 
so  small  as  to  form  only  a  small  part  of  the  wave- 
lengths, even  of  tones  of  high  pitch.  The  whole  of 
the  membraneous  labyrinth  may  be  regarded  as  part 
of  any  wave  acting  on  the  ear,  and  the  wave  is  not 
arrested  by  the  labyrinth  as  waves  of  light  are  arrested 
by  the  retina,  but  they  sweep  onwards  through  the 
bones  of  the  head.  The  fact  of  the  labyrinth  being 
so  small,  relatively  to  the  size  of  the  wave,  makes  no 
difference  in  the  result ;  so  that  the  labyrinth  is  acted 
on  in  the  same  way,  whether  the  ear  receives  a  wave 
of  thirty  feet  in  length,  such  as  is  produced  by  the 
longest  pipe  in  a  modern  organ,  or  a  wave  of  two- 
thirds  of  an  inch,  produced  by  the  highest  note  of  a 
piccolo  flute.  The  nerve-endings  are  very  much 
smaller,  but  they  also  act  as  minute  portions  of  any 
wave,  and  any  reasoning  as  to  the  effect  of  such 
waves  is  quite  irrespective  of  the  small  dimensions  of 
the  receiving  organs  in  the  internal  ear.  This  point 
is  of  great  importance  in  the  consideration  of  the 
theory  of  hearing  advanced  by  Helmholtz. 

It  is  clear,  then,  that  the  number  of  movements 
communicated  to  the  structures  in  the  internal  ear 
in,  say  a  second  of  time,  depends  on  the  pitch  of  the 
139 


HERMANN  VON  HELMHOLTZ 

note,  as  it  can  be  shown  experimentally  that  as  a 
note  rises  in  pitch  the  number  of  pressures  also  in- 
creases. Helmholtz,  for  this  and  other  purposes, 
improved  the  syren  of  Cagniard-de-la-Tour,  and 
invented  the  well-known  polyphonic  syren  now 
found  in  every  physical  and  physiological  laboratory. 
Another  way  of  looking  at  this  question  of  pitch  is 
to  say  that  it  depends  on  the  duration  of  the  indi- 
vidual pressures.  For  example,  the  variation  of  pres- 
sure involved  in  a  tone  of  256  vibrations  per  second 
will  last  the  -ai^th  of  a  second,  while  that  of  its 
octave  will  last  only  the  -5x2^  of  a  second.  It 
is  not  necessary,  therefore,  to  have  a  large  number 
of  pressures  per  second  to  arouse  a  sensation  of  a 
tone  of  a  certain  pitch ;  a  small  number,  possibly 
only  a  few,  if  they  come  at  a  given  rate,  will  be 
quite  sufficient.  If  now  we  suppose  that  there  are 
nerve-endings,  say  in  the  cochlea,  so  constructed  as 
to  have  each  its  own  period  of  vibration,  when 
pressures  come  in  at  a  certain  rate,  the  structures 
adapted  to  that  rate  will  be  thrown  into  action, 
and  we  can  conceive  movements  to  be  excited. 
These  movements  will  in  some  way  stimulate  the 
nerve-ending,  and  a  nervous  impulse  will  be  trans- 
mitted to  the  brain,  in  which  will  arise,  by  some 
molecular  process,  utterly  unknown,  the  sensation  of 
a  tone  of  that  pitch.  Again,  on  such  a  supposition, 
it  is  easy  to  explain  intensity  or  loudness.  This  will 
evidently  depend  on  the  amplitude  of  movement  of 
140 


HELMHOLTZ  IN  BONN 

the  base  of  the  stapes,  on  the  amplitude  of  the  ex- 
cursions of  the  vibratile  bodies  in  the  cochlea,  and 
on  the  degree  of  stimulus  given  to  the  nerve. 

The  base  of  the  stapes  is  chiefly  opposite  the 
utricle,  although  it  partly  abuts  against  the  saccule. 
On  the  wall  of  the  utricle,  immediately  in  front, 
there  are  no  nerve-endings  or  modified  epithelium, 
but  on  the  back  wall  we  find  a  ridge  called  the  crista 
acoustica,  on  which  are  long  cells  having  bristle-like 
points  which  are  directed  towards  the  base  of  the 
stapes.  In  front  of  these  bristle  cells  lies  a  mass  of 
otoliths,  or  ear  stones,  consisting  of  carbonate  of  lime. 
The  pressures  must  be  communicated,  in  the  first 
instance,  to  the,  otoliths,  and  by  them  to  the  bristle 
cells.  As  the  bristle  cells  are  fixed,  while  the  otoliths 
are  capable  of  moving  backwards  and  forwards  in  a 
fluid,  it  is  clear  that  one  impulse  from  the  base  of  the 
stapes  may  cause  the  otoliths  to  oscillate,  and,  by  thus 
making  a  series  of  impacts  on  the  points  of  the  bristle 
cells  produce  in  them  a  more  or  less  prolonged  ex- 
citation. This  was  the  opinion  of  Johannes  Miiller. 
Helmholtz,  on  the  contrary,  considered  the  matter 
from  the  physical  point  of  view,  and  his  opinion  was 
that  the  thin  membrane,  bearing  the  bristle  cells, 
will  readily  move  to  the  impacts  of  the  stapes,  and 
the  heavy  otolithic  mass,  by  virtue  of  its  inertia,  will 
move  more  slowly  at  first,  but  it  will  continue  to 
oscillate,  and  thus  keep  up  stimulation.  The  long 
and  extremely  light  bristles  also  appeared  to  him  to 
141 


HERMANN  VON  HELMHOLTZ 

be  well  adapted  for  sympathetic  resonance,  but,  as 
they  were  of  small  mass,  they  could  not  long  continue 
their  motion.  Again,  according  to  him,  the  am- 
pullae at  the  ends  of  the  semi-circular  canals,  in  which 
there  are  also  nerve-endings  similar  to  those  in  the 
crista,  being  wide  cavities  with  narrow  exits,  are 
suitable  for  producing  a  central  current,  which  partly 
passes  into  eddies,  and  these  would  deflect  the  bristles, 
causing  an  oscillation.  A  movement  of  the  whole 
mass  of  the  bristle,  floating  in  the  fluid,  would  not 
serve  the  same  purpose,  but  discontinuous  streams  of 
different  strengths  and  in  different  directions  would 
do  so  effectively.  Thus  Helmholtz  contributed  to 
our  knowledge  of  what  may  take  place  in  the  saccule 
and  utricle  and  ampullae.  Researches  made  since  his 
time  have  suggested  that  these  parts  may  not  have  to 
do,  strictly  speaking,  with  hearing,  but  with  the  re- 
ception of  those  greater  variations  of  pressure  on 
which  the  sense  of  equilibrium  depends.  They  may 
have  to  do  with  the  appreciation  of  mass  movement, 
and  only  indirectly  with  those  more  delicate  variations 
of  pressure  on  which  true  hearing  depends. 

Hitherto  we  have  considered  only  the  reception  of 
simple  harmonic  (sometimes  termed  simple  pendular) 
vibrations  which  are  known  to  be  physically  re- 
lated to  pure  tones.  The  sensation  of  a  pure  tone, 
such  as  can  be  excited  by  carefully  bowing  a 
tuning  fork,  mounted  on  a  resonance  box,  or  by 
an  open  organ  pipe  caused  to  sound  gently  by  a 
142 


HELMHOLTZ  IN  BONN 

steady  stream  of  air  at  low  pressure,  is  analogous  to 
that  of  a  pure  colour,  such  as  the  red,  green,  or  violet 
of  the  spectrum.  Such  tones,  however,  are  seldom 
heard,  the  majority  of  tones  being  compound  and 
analogous  to  mixtures  of  simple  colours,  such  as  red 
and  violet  producing  purple,  and  so  on.  This  fact 
was  long  known  to  writers  on  acoustics,  but  it  was 
Helmholtz  who  first  made  an  exhaustive  examination 
of  such  compound  tones,  and  pointed  out  their  im- 
portance in  connection  with  the  question  of  quality, 
timbre,  or  klangfarbe  (clang  tint),  as  he  termed  the 
nature  of  the  sensation  by  which  we  distinguish  one 
tone  from  another,  although  of  the  same  pitch  and 
of  the  same  intensity. 

If  we  help  the  mind  by  representing  to  ourselves 
the  varying  forms  of  waves  on  the  surface  of  water, 
some  with  long  smooth  backs,  others  with  narrow 
crests  and  longer  troughs,  some  with  the  slope  in 
the  ascent  sudden  and  with  others  more  gradual,  we 
see  that  there  may  be  an  almost  infinite  variety  of 
wave-forms.  ( By  the  term  '  wave-forms '  we  mean 
only  the  manner  in  which  the  changes  of  pressure  are 
represented  diagrammatically.)  So  it  is  with  sound. 
Instead  of  a  simple  pendular  vibration  we  may  have 
vibrations  or  pressures  of  complicated  form,  which  may 
cause  the  drumhead  to  move  outwards  and  inwards 
through  a  complicated  path  of  excursion.  These 
movements  correspond  to  the  action  of  a  compound 
wave.  Thus  pressures  of  a  similar  character  pass  into 
H3 


HERMANN  VON  HELMHOLTZ 

the  cochlea  and  sweep  over  the  nerve-endings.  The 
question  is,  how  does  the  cochlea  behave  in  such  cir- 
cumstances, and  will  its  action  explain  quality  of  tone  ? 
Helmholtz  attacked  the  problem  both  by  analysis 
and  by  synthesis.  In  the  first  place,  he  was  familiar 
with  Ohm's  l  application  in  1843  °f  Fourier's  principles 
to  the  decomposition  of  a  sound  wave  of  any  type 
into  a  number  of  simple  harmonic  vibrations,  each 
simple  harmonic  vibration  corresponding  to  a  simple 
tone  such  as  a  tuning  fork  approximately  gives. 
Fourier's 2  theorem  states  that  any  given  regular 
periodic  form  of  vibration  can  always  be  produced 
by  the  addition  of  simple  vibrations  having  vibra- 
tional  numbers  which  are  once,  twice,  three  times, 
etc.,  as  great  as  the  vibrational  number  of  the  given 
motion  ;  and  further,  if  we  know  the  amplitudes 
of  the  simple  vibrations  and  the  differences  of  phase, 
then  any  regular  periodic  motion  can  be  shown  to 
be  the  sum  of  a  certain  number  of  harmonic  vibra- 
tions ;  in  other  words,  the  compound  wave  may  be 
analysed  into  a  set  of  constituents  of  definite  periods. 
Applying  this  to  the  motion  of  the  air  close  to  the 
ear,  we  find  that  any  such  motion,  corresponding  to 
a  musical  tone,  may  be  always,  but  for  each  case 
only  in  a  single  way,  shown  to  be  the  sum  of  simple 
harmonic  motions,  corresponding  to  the  partial  tones 
of  this  compound  musical  tone. 

1  Poggendorff's  Annalen  der  Physik,  t.  lix.,  p.  513  ;  t.  Ixii.,  p.  i. 
1  Theorie  Analytique  de  laChaleur.     Paris,  1821. 
I44 


CHAPTER    XII 

HELMHOLTZ    IN    BONN    AND    HEIDELBERG SENSATIONS 

OF    TONE    CONTINUED 

HELMHOLTZ  showed  next  how  a  compound 
wave  of  sound  might  be  analysed  by  the 
application  of  the  principle  of  resonance.  The  air  in 
any  cavity  or  vessel,  such  as  a  bottle  with  a  narrow 
neck,  or  the  familiar  shell  held  to  the  ear,  which, 
in  the  days  of  childhood,  we  thought  gave  us  the 
sound  of  the  sea,  is  thrown  into  sympathetic  vibration 
by  the  vibrations  of  any  sounding  body  in  its  vicinity,  if 
the  vibration  periods  of  the  body  and  of  the  cavity  are 
approximately  the  same.  In  the  first  instance  Helm- 
holtz  used,  as  had  previously  been  done  by  Ohm,  two 
bottles,  with  fairly  wide  mouths  ;  and  then  the  size  of 
the  cavity  could  be  altered  by  filling  the  bottle  more 
or  less  full  of  water.  Streams  of  air  were  directed 
across  the  mouths  through  flattened  gutta-percha 
tubes.  The  bottles  were  tuned  to  b  and  £',  an 
interval  of  an  octave.  The  sound  of  the  first  bottle 
was  like  the  vowel  U,  but  when  the  sound  of  the 
K 


HERMANN  VON  HELMHOLTZ 

second  was  added  to  it  the  resultant  sound  was 
more  like  O.  Helmholtz  was  able  to  distinguish  the 
sounds  in  the  mixture.  This  experiment  suggested  the 
use  of  resonators.  These  were,  in  the  first  instance, 
cones  and  cylinders  made  of  pasteboard,  and  finally 
the  resonators,  in  the  hands  of  Rudolf  Konig,  a  native 
of  Konigsberg,  now  established  in  Paris,  took  the  form 
of  hollow  brass  globes,  each  with  a  narrow,  nipple- 
like  end,  which  was  introduced  into  the  ear,  while  the 
other  was  directed  to  the  source  of  sound.  By  the 
use  of  a  number  of  such  resonators,  each  tuned  to 
a  particular  tone,  it  is  possible  to  analyse  a  compound 
wave  of  sound  into  its  constituents.  However  com- 
plicated the  wave  may  be,  the  ear  will  pick  up  the 
tone  of  the  resonator,  and  this  tone  will  sound  loudly 
in  the  ear.  This  invention  was  of  the  greatest 
importance  in  practical  acoustics,  as  it  enabled  the 
observer  to  sift  a  mass  of  sound,  and  it  did  for  the  ear 
what  the  prism  of  Newton  did  for  the  eye.  Helm- 
oltz  also  worked  out  the  mathematical  theory  of 
resonance  in  great  detail.1  Many  years  ago  the 
writer,  with  a  feeling  of  veneration,  had  the  satis- 
faction of  seeing  the  original  resonators  of  Helm- 
holtz in  the  physiological  laboratory  of  Heidelberg. 

Helmholtz  then  laid  stress  on  the  fact,  that  the 
ear  is  capable  of  analysing  a  compound  tone,  even 
without  the  aid  of  resonators.  Musicians  and 

'For  an  exposition,  see  Lord  Rayleigh  on  Sound,  vol.  ii.,  p.  171. 
London,  1894. 

I46 


HELMHOLTZ  IN  BONN 

physicists  have  long  known  that  if  a  violin  string  is 
plucked,  and  attention  is  fixed  on  the  sensation  of 
tone,  we  not  only  hear  that  of  the  musical  tone 
whose  pitch  is  determined  by  the  period  of  the  large 
vibrations  of  the  string,  but  in  addition  to  this,  the 
ear  becomes  aware  of  a  whole  series  of  higher  musical 
tones,  called  the  harmonic  upper  partial  tones.  The 
first  one,  termed  the  fundamental  or  prime  partial 
tone,  or  the  prime,  is  the  lowest,  and  generally  the 
loudest,  of  all,  and  it  is  the  tone  by  whose  pitch  we 
judge  of  the  pitch  of  the  whole  compound  musical 
tone.  The  partials  are  so  arranged  that  the  first 
partial,  or  second  harmonic  constituent,  is  the  octave 
of  the  prime,  with  twice  the  number  of  vibrations ; 
the  second,  the  fifth  of  this  octave,  with  three 
times  the  number  of  vibrations ;  the  third,  the 
second  higher  octave,  with  four  times  the  number  of 
vibrations  ;  the  fourth,  the  major  third  of  the  second 
higher  octave,  with  five  times  the  number  of  vibra- 
tions of  the  prime  ;  the  fifth  is  the  fifth  of  the  second 
higher  octave,  or  a  minor  third  above  the  fourth 
partial,  with  six  times  the  number  of  vibrations  of 
the  prime  in  the  same  time.  Thus  the  partials  go 
on,  becoming  generally  fainter,  to  tones  making 
seven,  eight,  nine,  etc.,  times  as  many  vibrations  in 
the  same  time  as  the  prime.  We  may  also  avoid 
using  the  word  t  partials '  altogether,  and  call  the 
harmonic  constituents  the  first,  second,  third,  etc., 
harmonics. 

H7 


HERMANN  VON  HELMHOLTZ 

Helmholtz  had  forks  constructed,  the  frequencies  of 
which  were  in  the  order  of  a  harmonic  series,  beginning 
with  one  having  a  pitch  of  256  vibrations  per  second. 
These  were  then  Ut2(c),  Ut3  (<:'),  Sol3(/),  Ut4  (c"\ 
Mi4  (O,  Sol4  (/'),  l(b"\>  nearly),  Ut6  (<"'),  etc.  They 
were  mounted  on  resonance  boxes,  by  which  the  vol- 
ume of  sound  was  much  augmented.  Thus  any 
combination  of  the  partials  with  the  prime  could 
be  readily  obtained  by  suitable  bowing,  and  at  the 
same  time  while  the  compound  tone  fell  on  the  ear, 
the  observer  could  effect  an  analysis  by  means  of 
resonators.  Since  the  invention  of  this  method, 
Rudolf  Konig  has  adapted  his  beautiful  device  of 
manometric  flames,  aided  by  the  rotating  mirror  of 
Wheatstone,  for  the  demonstration  of  the  analysis  of 
a  compound  tone.1 

It  will  be  evident  that  various  combinations  of  the 
waves  of  the  prime  with  those  of  the  partials  will 
produce  varieties  of  wave  form,  and  that  the  form  of 
the  resultant  wave  will  be  modified  by  the  phase  and 
the  amplitude  of  the  constituent  waves.  But  we  have 
seen  that  the  ear  can  resolve  musical  tones  into  a 
series  of  partials,  and  that  it  behaves  in  accordance 
with  the  proposition  advanced  by  Ohm,  namely,  that 
the  human  ear  perceives  pendular  vibrations  alone  as 
simple  tones,  and  resolves  all  other  periodic  motions  of 
the  air  into  a  series  of  pendular  vibrations,  hearing 

1  For  a  figure  of  the  apparatus,  see  M'Kendrick's  Physiology,  vol  ii., 
p.  686. 

I48 


HELMHOLTZ  IN  BONN 

the  series  of  simple  tones  which  correspond  with  these 
simple  vibrations. 

The  interesting  question  now  arises,  whether  the  ear, 
having  to  deal  with  waves  varying  almost  infinitely  in 
form,  is  differently  affected  by  such  waves,  according  as 
their  form  represents  various  modes  of  pressure  (pushes 
and  pulls)  on  the  drumhead  and  conducting  mechanism  ? 
When  we  sound  the  harmonic  series  of  forks  from 
Ut  to  Ut5,  we  hear  a  rich  harmonious  sound,  and  we 
can  analyse  the  sensation,  and  pick  out  the  tone  of  any 
particular  partial,  more  especially  if  it  is  slightly 
strengthened  by  a  touch  of  the  bow.  By  varying  the 
order  and  intensity  of  the  partials,  we  can  produce  a 
very  large  number  of  wave-forms,  but  the  general 
character  of  the  harmonious  sound  remains  the  same. 
In  other  words,  waves  may  differ  much  in  form,  but 
if  they  contain  the  same  harmonic  constituents,  the, 
sensational  effect  will  be  the  same.  This  would 
appear  to  indicate  that  the  ear  takes  no  cognisance 
of  phase.  Helmholtz  invented  a  special  apparatus 
to  investigate  this  question.  This  costly  apparatus 
was  presented  to  him  by  King  Maximilian  of 
Bavaria.  It  consists  of  a  harmonic  series  of  forks, 
electrically  driven,  and  so  arranged  that  they  can  be 
sounded  in  any  order  and  with  various  intensities, 
according  to  changes  produced  in  the  size  of  the 
orifices  of  their  appropriate  resonators.1  The  resona- 

1  A  figure  of  the  apparatus  is  given  in  M'Kendrick's  Physiology,  vol. 
ii.,  p.  691. 

I49 


HERMANN  VON  HELMHOLTZ 

tors  may  thus  be  put  slightly  out  of  tune,  their 
resonance  is  weakened,  and  thus  the  phase  is  altered. 
Helmholtz  stated  the  result  as  follows  : — '  Differences 
in  musical  quality  depend  solely  on  the  presence  and 
strength  of  partial  tones,  and  in  no  respect  on  the 
difference  in  phase  under  which  these  partial  tones 
enter  into  composition.'  This  statement  has  been  dis- 
puted by  Lord  Kelvin,  on  theoretical  grounds,  and  by 
Rudolf  Konig,  who  has  submitted  it  to  the  test  of 
experiment ;  but  Lord  Rayleigh  remarks,  regarding 
Konig's  experiment,  *  the  results  are  in  harmony  with 
the  view  that  would  ascribe  the  departure  from  Ohm's 
law,  involved  in  any  recognition  of  phase  relations,  to 
secondary  causes.' l  Physically,  timbre  must  be  due  to 
the  form  of  the  vibration  curve,  otherwise  telephoning 
would  be  impossible  ;  but  the  ear  always  analyses  the 
curve  into  its  constituents. 

With  the  view  of  establishing  his  theory  of  hearing 
on  a  firm  basis,  Helmholtz  made  a  careful  examination 
of  the  question  of  the  existence  of  damping  arrange- 
ments in  the  ear.  Suppose  tones  are  pouring  into  the 
ear  in  rapid  succession,  and  that  the  effect  of  one  tone 
has  not  died  away  before  the  influence  of  the  next  one 
is  felt,  musical  effect  would  be  disturbed.  This  would 
certainly  occur  if  we  executed  a  shake  on  a  piano  of 
eight  or  ten  notes  in  a  second,  so  that  each  note  would 
be  sounded  four  or  five  times.  But  it  is  well  known 
that  the  sensation  excited  by  such  shakes  is  rough  and 

1  Rayleigh,  of.  cit.,  vol.  ii.,  p.  469. 
ISO 


HELMHOLTZ  IN  BONN 

unpleasant,  indicating,  in  the  opinion  of  Helmholtz, 
4  that  the  vibrating  parts  of  the  ear  are  not  damped  with 
sufficient  force  and  rapidity  to  allow  of  successfully 
effecting  such  rapid  alternation  of  tone.  It  is  there- 
fore highly  probable  that  a  damping  mechanism  exists.' 

The  next  step  was  to  attempt  to  explain  how  the 
cochlea,  in  which  the  nerve-endings  exist  in  the  form 
of  the  remarkable  organ  of  Corti,  can  analyse  tone, 
and  with  the  development  of  this  theory,  however 
much  it  may  have  to  be  modified  as  time  goes  on, 
the  name  of  Helmholtz  will  be  imperishably  con- 
nected. There  are  only  three  ways  in  which  the  nerve- 
endings  may  be  affected.  Either  (i)  small  vibratile 
bodies  may  exist  so  as  to  transmit  the  pressures  sent 
to  the  filaments  of  the  auditory  nerve,  each  vibra- 
tile body  having  a  frequency  period  of  its  own  ;  or 
(2)  individual  nerve  fibres  may  be  directly  excited 
by  waves  of  a  definite  period,  that  is  to  say,  there 
may  be  differences  in  the  nerve  fibres,  so  that  they 
have  a  selective  action  ;  or  (3)  the  organ  may  be 
affected  as  a  whole,  all  the  nerve  fibres  being  affected 
by  any  variations  of  pressures,  and  thus  the  power 
of  analysis,  which  is  admitted,  would  be  relegated 
from  the  peripheral  to  the  cerebral  organs. 

The  first  hypothesis  seems  a  priori  to  be  probable, 
for  the  following  reasons: — (i)  The  existence  of 
such  bodies  would  give  a  natural  explanation  of  many, 
if  not  all,  of  the  phenomena  ;  (2)  the  evidence  of 
comparative  physiology  points  to  gradually-increasing 


HERMANN  VON  HELMHOLTZ 

complexity  in  the  structure  of  all  the  terminal  organs 
of  special  sense,  as  if  there  arose  a  necessity  for 
differentiation  and  discrimination  in  the  effects  of 
various  kinds  of  stimuli ;  and  (3)  investigations  into 
the  action  of  all  the  sense  organs,  such  as  those  of 
touch  and  temperature  in  the  skin,  of  light  and  colour 
in  the  retina,  of  taste  in  the  tongue,  and  of  smell  in 
the  olfactory  region,  all  indicate  specialization  of 
function  in  the  peripheral  apparatus. 

Although  the  conception  that  vibrators  exist  in 
the  cochlea  flitted  before  the  minds  of  Thomas 
Young,  John  and  Charles  Bell,  and  Johannes  Miiller, 
it  was  first  clearly  put  forward  by  Helmholtz.  It 
may  be  shortly  stated  as  follows  : — (i)  In  the  cochlea 
there  are  vibrators,  tuned  to  frequencies  within  the 
limits  of  hearing,  say  from  30  to  40,000  or  50,000  vibra- 
tions per  second  ;  (2)  each  vibrator  is  capable  of  exciting 
its  appropriate  nerve  filament  or  filaments,  so  that  a 
nervous  impulse,  corresponding  to  the  frequency  of 
the  vibrator,  is  transmitted  to  the  brain, — not  corre- 
sponding necessarily  as  regards  the  number  of  nervous 
impulses,  but  in  such  a  way  that  when  the  impulses 
along  a  particular  nerve  fibre  reach  the  brain,  a  state  of 
consciousness  is  aroused  which  does  correspond  with 
the  number  of  the  physical  stimuli,  and  with  the 
period  of  the  auditory  vibrator  ;  (3)  the  mass  of  each 
vibrator  is  such  that  it  will  be  easily  set  in  motion, 
and  after  the  stimulus  has  ceased  it  will  readily  come 
to  rest ;  (4)  damping  arrangements  exist  in  the  ear, 
152 


HELMHOLTZ  IN  BONN 

so  as  to  quickly  extinguish  movements  of  the  vibrators  ; 
(5)  if  a  simple  tone  falls  on  the  ear,  there  is  a  pendular 
movement  of  the  base  of  the  stapes,  which  will  affect 
all  the  parts,  causing  them  to  move  ;  but  any  part 
whose  natural  period  is  nearly  the  same  as  that  of  the 
sound  will  respond  on  the  principle  of  sympathetic 
resonance,  a  particular  nerve  filament  or  nerve  fila- 
ments will  be  strongly  affected,  and  a  sensation  of  a 
tone  of  a  definite  pitch  will  be  experienced,  thus 
accounting  for  the  discrimination  of  pitch  ;  (6)  intensity 
or  loudness  will  depend  on  the  amplitude  of  movement 
of  the  vibrating  body,  and  consequently  on  the 
intensity  of  nerve  stimulation  ;  (7)  if  a  compound 
wave  of  pressure  be  communicated  by  the  base  of  the 
stapes,  it  will  be  resolved  into  its  constituents  by  the 
vibrators  corresponding  to  the  tones  existing  in  it, 
each  vibrator  picking  out  its  appropriate  constituent 
and  thus  irritating  its  corresponding  nerve  filament,  so 
that  nervous  impulses  are  transmitted  to  the  brain, 
where  they  are  fused  in  such  a  way  as  to  give  rise 
to  a  sensation  of  a  particular  quality  or  character,  but 
still  so  imperfectly  fused  that  each  constituent,  by  a 
strong  effort  of  attention,  may  be  specially  recognised. 
This  last  statement  affords  an  explanation  of  the 
analytic  powers  of  the  ear. 

Now    the   structure    of   the    ductus   cochlearis,    in 

which    the   nerve-endings   exist,  meets   the  demands 

of  this    theory.     It    is  highly  differentiated,  and    its 

parts  appear  suitable  for  executing  independent  vibra- 

J53 


HERMANN  VON  HELMHOLTZ 

tions.  The  minute  size  of  the  structures  does  not 
present  any  difficulty  ;  because,  however  minute  the 
vibrators  might  be,  if  they  had  different  periods,  they 
must  act  in  obedience  to  the  same  principles  of 
resonance  as  larger  bodies  do  outside  the  ear.  In 
1863,  Helmholtz  was  of  opinion  that  the  different 
degrees  of  tension  in  the  arches  of  Corti  indicated 
capacity  for  vibrating  at  different  periods.  Soon 
after,  it  was  shown  by  Hasse  that  these  rods  do  not 
exist  in  birds,  animals  presumably  capable  of  appre- 
ciating tones ;  and  Hensen  pointed  out  that  the 
membrana  basilaris,  on  which  the  rods  rest,  consisted 
of  transverse  fibres,  which  varied  in  length  approxi- 
mately from  -g^jth  of  an  inch,  at  the  base  of  the  cochlea, 
to  -6Vh  of  an  inch  at  its  apex.  This  led  Helmholtz 
to  suggest  that  it  is  probably  the  breadth  of  the 
membrana  basilaris  in  the  cochlea  which  determines 
the  tuning.  He  pointed  out  that  the  membrane 
was  in  a  state  of  tension  transversely,  while  it  has 
only  little  tension  in  the  longitudinal  direction,  and 
that  such  a  membrane  had  very  different  properties 
from  that  of  a  membrane  which  had  the  same  tension 
in  all  directions.  The  membrane,  in  fact,  behaves 
like  a  system  of  stretched  strings,  bound  together  by 
a  semifluid  substance.  Each  string  or  fibre  would 
act  independently  of  the  others,  and  would  be  set 
into  vibration  by  an  impulse  to  the  fluid  in  the  scala 
vestibuli,  corresponding  to  its  period.  Consequently, 
if  a  part  of  the  membrane  were  called  into  action,  one 
154 


HELMHOLTZ  IN  BONN 

of  its  radial  fibres,  which  corresponded  to  the  exciting 
tone,  would  vibrate,  and  the  vibrations  would  extend 
with  diminishing  strength  on  the  adjacent  portions  of 
the  membrane.  Possibly  some  of  the  structures  on 
the  surface  of  the  membrane  might  act  as  dampers. 
In  this  way  the  parts  of  the  membrane  near  the  base 
of  the  cochlea  would  be  adapted  for  the  higher,  while 
those  near  the  vertex  of  the  cochlea  would  be  suitable 
for  the  deeper  tones.  Corti's  arches  are,  therefore,  of 
secondary  importance,  serving  either  as  supporting 
structures,  or  for  transmitting  vibrations  of  parts  of 
the  basilar  membrane  to  the  rows  of  hair  cells  placed 
on  their  backs. 

Helmholtz  also  discussed  the  question  as  to  whether 
histological  evidence  as  to  the  number  of  possible 
vibratile  structures  is  such  as  will  satisfy  the  demands 
of  theory.  He  attempted  to  answer  this  question  on 
the  basis  of  E.  H.  Weber's  statement,  that  practised 
musicians  can  *  perceive  even  a  difference  of  pitch 
for  which  the  vibrational  numbers  are  as  1000  to 
1001,'  or  the  -$fth  of  a  semitone,  a  smaller  interval 
than  that  between  two  of  Corti's  arches,  on  the 
assumption  that  there  are  about  33^  for  each  semitone 
in  each  cochlea  ;  and  he  accounted  for  the  apparent 
deficiency  by  the  explanation,  that  if  a  tone  came  in 
between  the  pitch  of  two  of  the  arches,  'it  would 
set  them  both  in  sympathetic  vibration,  and  the  arch 
would  vibrate  the  more  strongly  which  was  nearest 
in  pitch  to  the  proper  tone.'  This  would  also  ex- 


HERMANN  VON  HELMHOLTZ 

plain  how  it  is  that  when  we  listen  to  the  syren,  as 
its  disc  revolves  faster  and  faster,  our  sensations  go 
on,  not  by  leaps  and  bounds,  but  continuously.  Since 
the  time  when  Helmholtz  wrote,  histological  evidence 
has  accumulated,  the  rods  and  arches  of  Corti,  the 
fibres  of  the  membrana  basilaris,  the  hairs  cells,  and 
even  the  nerve  fibres  in  each  auditory  nerve,  have  been 
counted,  and  it  has  been  conclusively  established  that 
there  is  in  the  cochlea  a  sufficient  number  of  possible 
vibratile  masses  to  satisfy  this  theory. 

He  then  proceeded  to  examine  the  cause  of  con- 
sonance and  dissonance,  and  to  apply  his  theory  in  ex- 
planation. If  we  sound  simultaneously  two  forks  that 
are  in  unison,  the  waves  coincide  and  one  sound  is 
heard  ;  but  if  the  pitch  of  one  of  the  forks  is  slightly 
flattened,  the  waves  do  not  coincide,  and  there  are 
maxima  and  minima.  A  rapid,  rattling,  beating  sound 
will  then  be  heard,  as  if  there  were  individual  thuds 
on  the  ear.  If  the  forks  are  nearly  the  same  in  pitch, 
the  beat,  as  it  is  termed,  will  be  heard  as  a  rising 
and  falling  in  the  intensity  of  the  sound,  and  as  the 
difference  in  pitch  between  the  forks  is  increased, 
there  is  also  an  increase  in  the  number  of  the  beats. 
If  such  beats  are  few  in  number,  so  as  to  be  readily 
counted,  the  sensation  of  waxing  and  waning  is  not 
disagreeable  ;  but  if  they  are  sufficiently  numerous, 
it  may  be  impossible  to  count  them,  and  the  sensation 
is  disagreeable.  Such  a  sensation  is  that  of  disson- 
ance. Helmholtz  found  the  sensation  to  be  most 
156 


HELMHOLTZ  IN  BONN 

disagreeable  when  the  ear  is  affected  by  about  33 
beats  per  second  ;  if  they  are  more  numerous,  the 
sensation  is  rough  and  unpleasant.  Further,  even 
when  the  frequency  of  beats  is  much  greater  than 
the  number  of  vibrations  required  to  produce  the 
sensation  of  a  tone,  the  sensation  is  never  uniform, 
but  is  of  a  rough,  intermittent  character. 

If  now  we  sound  an  interval  on  an  instrument 
giving  forth  compound  tones,  such,  for  example, 
as  an  octave,  each  note  will  have  its  corresponding 
partials ;  and  as  these  come  closer  and  closer  to- 
gether the  higher  they  are  in  the  series,  it  is 
clear  that  they  may  come  within  beating  distance, 
and  thus  give  a  certain  harshness  to  the  sound. 
The  beating  distance  may,  for  tones  of  medium  pitch, 
be  roughly  fixed  at  a  minor  third ;  this  interval, 
of  course,  will  expand  for  intervals  in  low,  and 
contract  for  intervals  in  high  ranges  of  the 
scale.  Thus,  the  same  interval  in  the  lower 
part  of  the  scale  may  give  slow  beats  that  are 
not  disagreeable,  while  in  the  higher  part  it 
may  cause  harsh  and  unpleasant  dissonance.  Two 
given  notes  will  produce  this  l  beating '  harshness 
when  the  difference  of  their  vibration  number  is 
about  70  or  80.  Thus  a  minor  third  will  sound 
pleasant  in  the  higher  ranges  of  the  scale.  There 
will  be  a  slight  roughness  at  medium  pitches  ;  while 
in  the  lower  ranges  there  will  be  harshness  and 
possibly  perceptible  beating.  On  the  other  hand,  if 
157 


HERMANN  VON  HELMHOLTZ 

the  interval  be  small,  say  a  semitone,  the  beating,  in 
the  lower  part  of  the  scale,  may  be  so  slow  as  not  to 
be  disagreeable,  whereas  in  the  higher  part  it  may 
cause  harsh  and  unpleasant  dissonance.  The  sensa- 
tional effect  of  beats  then  depends  rather  on  the 
difference  of  the  vibration  numbers  than  on  the  interval. 
As  a  rule,  the  partials  up  to  the  seventh  are  beyond 
beating  distance,  but  above  this  they  soon  come  close 
together.  In  the  neighbourhood  of  the  tenth,  the 
interval  may  be  about  a  tone,  of  the  sixteenth,  a 
semitone,  and  still  higher  they  come  together  so  as 
to  cause  dissonance.  This  fact  explains  why  intervals 
sound  so  harsh  when  produced  by  reeds,  the  sounds 
of  which  are  rich  in  upper  partials,  and  also  the 
harsh  but  brilliant  quality  of  intervals  sounded  on 
two  trumpets.  Intervals  even  when  produced  on 
instruments  giving  compound  tones  with  few  har- 
monic constituents,  such  as  flutes,  have  still  their 
own  character.  Helmholtz  applied  his  theory  with 
consummate  skill,  not  only  as  an  explanation  of 
the  quality  of  musical  tones  in  many  instruments, 
the  human  larynx  included,  but  also  of  the  satisfying 
character  of  certain  musical  intervals,  as  contrasted 
with  the  discordant  character  of  others.  Thus 
unison  y,  minor  third  £,  major  third  £,  fourth  ^,  fifth 
-f ,  minor  sixth  -f ,  major  sixth  f ,  and  octave  f ,  are  all 
concords  ;  while  a  second  £,  minor  seventh  y,  and 
major  seventh  y,  are  discords.  The  smoothest  in- 
terval is  the  octave,  next  the  fifth,  then  the  fourth, 
158 


HELMHOLTZ  IN  BONN 

major  third,  and  so  on.  What  he  did  not  explain 
is — Why  the  sensation  should  be  disagreeable  when 
two  portions  of  the  membrana  basilaris,  sufficiently 
near,  are  thrown  into  vibration  ?  For  some  un- 
explained reason,  if  two  nerve  filaments  sufficiently 
near  are  simultaneously  stimulated,  or  if  they  are 
stimulated  in  the  intermittent  manner  peculiar  to 
beats,  the  sensation  is  disagreeable.  Helmholtz 
contrasts  it  with  that  caused  by  a  flickering  light 
on  the  eye.  There  is,  in  listening  to  beats,  always  an 
effort  at  analysis,  and  it  may  be  that  this  effort  gives 
rise  to  a  disagreeable  sensation  when  the  number  of 
beats  reaches  a  certain  amount. 

While  the  theory  explains  the  dissonance  of  in- 
tervals produced  by  instruments  that  are  rich  in 
partials,  how  does  it  apply  to  cases  in  which  there  are 
no  partials,  but  only  prime  tones,  as  when  the  tones 
are  produced  by  well-bowed  tuning-forks  and  open 
organ  pipes  ?  This  question  also  was  attacked  by 
Helmholtz,  and  led  to  the  examination  of  what  he 
termed  combination  tones.  If,  for  example,  two 
forks  representing  a  fifth  are  properly  bowed,  sound- 
ing the  fork  of  lower  pitch  first  and  that  of  higher 
pitch  afterwards,  we  may  hear  a  weak  lower  tone, 
the  pitch  of  which  is  an  octave  below  that  of  the 
first  fork.  This  is  known  as  a  combination  tone. 
Such  tones  he  divided  into  two  classes — differential 
notes,  in  which  the  frequency  is  the  difference  of  the 
frequencies  of  the  generating  tones  ;  and  summational 
159 


HERMANN  VON  HELMHOLTZ 

tones,  having  a  frequency  which  is  the  sum  of  those 
of  the  tones  producing  them.  Then,  when  a  fifth 
is  sounded,  the  differential  tone  is  an  octave  below  the 
low  note  ;  with  a  fourth  it  is  a  twelfth  j  with  a  major 
third,  two  octaves  ;  with  a  minor  third,  two  octaves  and 
a  major  third  ;  with  a  major  sixth,  a  fifth  ;  and  with 
a  minor  sixth,  a  major  sixth.  Such  differential  tones, 
first  heard  by  Sorge  about  1740,  are  usually  associated 
with  the  name  of  Tartini.  Summational  tones  were 
discovered  by  Helmholtz.  It  is  clear  that  there  must 
be  differential  tones  of  several  orders,  according  as 
they  are  produced  between  the  generating  tones  them- 
selves, then  between  the  differential  tone  and  each 
of  the  generators,  and  so  on.  It  is  not  difficult  to 
detect  differential  tones,  but  this  is  not  the  case  with 
summational  tones.  Helmholtz,  who  had  a  remark- 
ably acute  and  well-trained  ear,  heard  them  first  with 
the  polyphonic  syren  and  the  harmonium,  and  after- 
wards with  organ  pipes  and  tuning-forks.  On  the 
other  hand,  Hermann  and  others  assert  that  they 
cannot  hear  these  tones.  There  can  be  little  doubt, 
however,  that  both  kinds  of  combination  tones  may  have 
an  existence  outside  of,  and  quite  independent  of,  the 
ear.  Helmholtz  states  that  c  whenever  the  vibrations 
of  the  air  or  of  other  elastic  bodies,  which  are  set  in 
motion  at  the  same  time  by  two  generating  simple 
tones,  which  are  so  powerful  that  they  can  no  longer 
be  considered  infinitely  small,  mathematical  theory 
shows  that  vibrations  of  the  air  must  arise  which  have 
j6o 


HELMHOLTZ  IN  BONN 

the  same  vibrational  numbers  as  the  combination 
tones.'  *  Recently  Riicker  and  Edser  have  demon- 
strated the  objective  existence  of  such  tones.2  Com- 
binational tones  may,  however,  as  Helmholtz  clearly 
showed,  be  produced  in  the  ear  itself,  because  of  the 
elastic  asymmetry  of  the  drum» 

The  importance  of  these  combinational  tones  in  the 
theory  of  hearing  is  obvious.  If  the  ear  can  only 
analyse  compound  waves  into  simple  pendular  vibra- 
tions, in  a  certain  order,  how  can  it  detect  combina- 
tional tones,  which  no  doubt  can  be  heard,  and  yet  do 
not  belong  to  that  order  ?  For  example,  when  the  in- 
terval is  harmonic  (400,  500)  the  combined  wave-forms 
make  a  wave  of  100  of  frequency,  so  that  the  ear,  like 
Fourier's  theorem,  may  easily  pick  out  this  tone  ;  but 
how  will  it  deal  with  intervals  of  incommensurate 
numbers,  such  as  407,  483  ?  Yet  this  combination 
tone  of  a  frequency  of  76  will  be  heard  as  distinctly  as 
one  arising  from  two  tones  having  frequencies  of  400 
and  500.  This  is  still  a  great  difficulty,  as  it  cannot 
be  said  that  experiments  made  by  many  others  since 
the  time  of  Helmholtz  have  removed  it.  Experiment 
shows  that  combinational  tones  are  produced  when  the 
notes  of  intervals  are  sounded  strongly  on  instruments 
like  tuning-forks,  whose  notes  are  nearly  simple  tones, 
free  from  upper  partials  ;  and  that  these  combinational 
tones  may  produce  beats  with  any  of  the  generators,  or 
among  themselves ;  and  these  beats,  feeble  as  they 

1  Sensations  of  Tone,  trans,  by  Ellis,  p.  235.       *  PAH.  Mag.,  April  1895. 

L 


HERMANN  VON  HELMHOLTZ 

may  be,  produce  that  feeling  of  less  and  less  con- 
sonance until  we  come  to  intervals  that  are  truly 
dissonant.  One  might  suppose  that  in  the  case  of 
tones  that  abound  in  partials,  combinational  tones 
might  be  produced  by  the  partials,  and  thus  a  new  source 
of  beats  might  lead  to  confusion  and  discord  ;  but 
theory  shows  that  dissonance  due  to  combinational 
tones,  produced  between  partials,  never  occurs  except 
when  it  has  already  taken  place  by  the  action  of  the 
partials  among  themselves.1 

Closely  connected  with  this  subject  is  the  investiga- 
tion of  the  cause  of  the  quality  of  the  human  voice, 
more  especially  as  to  vowel  tones.  This  also  engaged 
the  attention  of  Helmholtz,  and  it  was  treated  by 
him  in  his  usual  masterly  fashion.2  Why  should  a 
vowel,  spoken  or  sung,  always  have,  even  with  the 
voices  of  different  persons,  the  same  quality,  so  that 
we  have  no  difficulty  in  distinguishing  A  from  E  and 
E  from  O  ?  Donders 3  was  the  first  to  show  that  the 
cavity  of  the  mouth,  as  arranged  for  the  giving  forth 
of  a  vowel,  was  tuned  as  a  resonator  for  a  tone  of 
a  certain  pitch,  and  that  different  pitches  corresponded 
to  the  forms  of  the  cavity  for  the  different  vowels. 
This  he  discovered,  not  by  the  use  of  tuning-forks, 
but  by  the  peculiar  noise  produced  in  the  mouth  when 
the  different  vowels  are  whispered.  The  cavity  of 

1  Sedley  Taylor,  Sound  and  Music.     London,  1873. 
3  Gel.  An%.  d.  k.  bayer  Acad.  d.  Wiaentch,  1859. 
3  De  Phytlologie  der  Spraak  klanken,  1870,  s.  9. 
162 


HELMHOLTZ  IN  BONN 

the  mouth  is  then  blown  like  an  organ  pipe,  and  by 
its  resonance  reinforces  the  corresponding  partials  in 
the  rushing  wind-like  noise.  Helmholtz  adopted 
another  method.  To  determine  the  pitch  of  the 
cavity  of  the  mouth,  considered  as  a  resonance  cavity, 
he  struck  tuning-forks  of  different  pitches,  and  held 
them  before  the  opening  of  his  mouth.  Then,  the 
louder  the  proper  tone  of  the  fork  was  heard  the 
nearer  l  it  corresponded  with  one  of  the  proper  tones 
of  the  included  mass  of  air.'  As  the  shape  of  the 
mouth  could  be  altered  at  pleasure,  according  to  the 
vowel  to  be  emitted,  it  was  easy  to  discover  the  pitch 
of  the  included  mass  of  air  for  each  vowel.  He  came 
to  the  conclusion  that  'the  pitch  of  the  strongest 
resonance  of  the  oral  cavity  depends  solely  upon  the 
vowel  for  pronouncing  which  the  mouth  has  been 
arranged.'  He  also  found  the  same  resonances  for 
men  as  for  women  and  children.  He  then  carefully 
examined  the  form  of  the  oral  cavity  for  each  vowel, 
and  showed  how  very  slight  changes  could  account 
for  the  quality  being  slightly  altered  for  different 
dialects.  He  also  demonstrated  that  the  tones  of 
the  human  voice  are  adapted  to  the  powers  of  the 
human  ear.  The  ear,  by  its  resonating  powers, 
favours  the  development  of  these  partials,  especially 
the  higher  ones,  which  give  a  peculiar  character  to 
human  tones.  His  theory  as  to  vowel-tone  is  summed 
up  in  the  following  sentence  : — *  Vowel  qualities  of 
tone  consequently  are  essentially  distinguished  from 
163 


HERMANN  VON  HELMHOLTZ 

the  tones  of  most  other  musical  instruments,  by  the 
fact  that  the  loudness  of  their  partial  tones  does  not 
depend  upon  the  numerical  order,  but  upon  the 
absolute  pitch  of  those  partials ;  thus,  if  I  sing  the 
vowel  A  to  the  note  £[7,  the  reinforced  tone  b"\>  is 
the  twelfth  partial  tone  of  the  compound  ;  and  when 
I  sing  the  same  vowel  A  to  the  note  b'fr,  the  rein- 
forced tone  is  still  £"[?,  but  is  now  the  second  partial 
of  the  compound  tone  sung.' '  He  also  endeavoured  to 
reproduce,  but  with  imperfect  success,  the  tones  of 
vowels  by  means  of  the  same  apparatus  as  he  employed 
in  the  investigation  of  the  influence  of  phase  (p.  149). 
The  theory  of  the  absolute  pitch  of  vowels,  as  advocated 
by  Helmholtz,  has  met  with  great  opposition,  and  to 
it  is  opposed  the  theory  of  relative  pitch,  but  space 
forbids  a  critical  examination  of  the  subject.2 

These  important  investigations,  the  results  of  which 
appeared  from  time  to  time,  mostly  after  he  had 
settled  in  Heidelberg,  were  collected  by  Helmholtz 
into  his  great  book  on  Sensations  of  Tone,  and  formed 
Parts  I.  and  II.  Part  III.  is  occupied  with  a  discus- 
sion of  the  relationship  of  musical  tones,  the  different 
principles  of  musical  style  in  the  development  of  music, 
the  tonality  of  homophonic  music,  the  music  of  the 
Greeks,  consonant  triads,  keys,  discords,  the  laws  of 
progression,  and  the  aesthetical  relations  of  the  whole 

1  Sensations  of  Tone,  p.  172. 

2  Discussed  in  article  on  Vocal  Sounds  in  Schaffer's  Text  Book,  vol.  ii., 
p.  59,  by  M'Kendrick  and  Gray. 

I64 


HELMHOLTZ  IN  BONN 

subject.  The  mere  enumeration  of  the  subjects 
discussed  will  give  one  a  faint  idea  of  the  breadth  and 
fulness  of  this  magnificent  work.  And  yet  even  all 
this  was  only  a  part  of  the  labours  of  Helmholtz  in 
acoustics.  As  already  mentioned,  there  is  scattered 
throughout  the  volume,  and  in  appendices,  numerous 
examples  of  a  mathematical  treatment  of  the  subject 
under  discussion.  In  addition,  we  have  papers  on  the 
motion  of  the  strings  of  a  violin,  communicated, 
during  one  of  Helmholtz's  visits  to  his  friend  Lord 
Kelvin,  then  Professor  William  Thomson,  to  the 
Philosophical  Society  of  Glasgow,  on  igth  December 
1860.  In  this  paper  he  fully  discussed  and  repre- 
sented graphically  the  course  of  the  vibration.1  As 
already  mentioned,  he  investigated  mathematically 
the  theory  of  damping,  and  calculated,  for  various 
intervals,  the  number  of  vibrations,  after  which  the 
intensity  of  a  free  vibration  is  reduced  to  one-tenth. 
He  estimated  also  the  pitch  of  the  partials  produced 
immediately  after  a  tuning-fork  has  been  struck.  He 
invented  an  electric  interrupter,  so  as  to  produce  an 
intermittent  current  in  the  best  way  and  without 
making  a  noise  by  the  production  of  sparks.  He 
discussed  the  reciprocal  relations  of  sounds,  showing 
that  a  sound  originating  at  one  point  is  perceived  at 
another  point,  even  if  there  are  obstacles  between  the 
two  points,  with  the  same  intensity  as  if  it  originated 
at  the  last  point  and  was  perceived  at  the  first ;  just  as 

1  See  also  Rayleigh's  Theory  of  Sound t  op.  cit^  vol.  i.,  p.  231. 
I65 


HERMANN  VON  HELMHOLTZ 

in  optics,  if  one  point  can  be  seen  from  a  second,  the 
second  can  also  be  seen  from  the  first.  Sound  shadows 
may  thus  be  produced,  but  they  are  only  partial,  in 
consequence  of  the  wave-lengths  of  sound  being  great 
in  comparison  with  the  sizes  of  ordinary  obstacles.  In 
connection  with  this  subject,  in  1860,  he  published  an 
important  paper,  in  which  he  examined  the  movements 
of  the  air  in  open  organ  pipes,  and  extended  Green's 
well-known  theorem,  the  chief  application  of  which 
belongs  to  Statical  Electricity.1  He  gave  the 
correct  theory  for  the  open  organ  pipe.  Lagrange, 
Daniel  Bernoulli,  and  Euler  assumed  that  at  the  open- 
ing the  pressure  could  not  vary  with  that  of  the 
surrounding  atmosphere  ;  but  Helmholtz  showed  that 
in  ordinary  cases  the  inertia  of  the  air  outside  the  pipe 
has  the  effect  of  practically  diminishing  its  length. 
He  also  took  into  account  the  friction  of  the  air 
against  the  walls  of  the  tube,  a  point  omitted  by  his 
predecessors.  He  also  investigated  some  of  the  con- 
ditions under  which  the  hammer  of  the  pianoforte 
strikes  the  strings.  He  invented  a  vibration  micro- 
scope for  the  examination  of  vibrating  points  on  any 
body,  say  a  violin  string,  so  as  to  see  the  well-known 
figures  of  Lissajous.  He  established  the  mathematical 
relation  of  velocity  and  density  in  the  propagation 
of  small  disturbances  in  gas  or  air. 

As  already  mentioned,  he  examined  mathematically 
the  laws  that  regulate  the  actions  of  resonators  of  various 

1  Rayleigh,  op,  cit.t  vol.  ii.,  p.  145. 

1 66 


HELMHOLTZ  IN  BONN 

forms  and  with  variously-shaped  apertures.  He  investi- 
gated the  special  mode  of  action  of  many  musical  instru- 
ments, and  in  particular,  divided  those  having  tongues 
into  inbeating  and  outbeating.  In  the  first  case  the 
passage  is  opened  when  the  tongue  moves  inwards, 
that  is  against  the  wind,  as  happens  in  the  clarinette. 
Lip  instruments,  such  as  the  trombone,  belong  to  the 
second  class,  the  passage  being  open  when  the  lips  are 
moved  outwards  or  with  wind.1  It  may  be  said  that 
the  whole  theory  of  the  mode  of  action  of  tongue 
pipes  is  due  to  Helmholtz.  He  also  gave  a  formula 
for  the  velocity  of  sound  in  narrow  tubes. 

When  Helmholtz  first  heard  of  the  telephone,  he 
remarked  to  Du  Bois  Reymond  : — c  The  invention 
seems  so  self  evident,  that  I  do  not  consider  it  necessary 
to  advance  a  theory.  Of  course,  I  have  for  years  gone 
to  bed  with  Fourier's  theorem  in  my  head,  and  I  have 
got  up  with  it  still  there,  so  I  must  not  judge  others 
by  myself.'  His  friend  observes,  that  possibly  it  was 
on  one  of  these  nights  that  he  was  obliged  to  get  up 
and  lull  his  intellect  by  playing  Bach's  fugues  on  a 
magnificent  grand  piano  presented  to  him  by  Messrs 
Steinway  of  New  York  in  recognition  of  his  services 
to  music.  On  another  occasion,  he  was  interested 
and  amused  by  the  delightful  experiment  of  causing  a 
highly-trained  vocalist  to  sing  the  vowels  with  the 
dampers  off  the  strings,  when  of  course  they  were 
returned  little  changed  in  quality.  From  the  time 

1  Rayleigh,  op.  cit.,  vol.  ii.,  p.  234. 
I67 


HERMANN  VON  HELMHOLTZ 

when  Pythagoras  is  said  to  have  discovered  the  arrange- 
ment of  tones  in  an  octave,  by  observing  that  the 
sounds  of  the  blacksmith's  hammer  in  the  forge  pro- 
duce a  fourth,  a  fifth  and  an  octave,  and  was  then  led 
to  obtain  harmonic  proportion  between  the  strings  of 
the  heptachord,  all  who  investigate  musical  tones 
know  that,  although  these  are  fleeting  sensations,  they 
depend  physically  on  numerical  relations  between 
various  kinds  of  movements  j  but  it  was  Helmholtz, 
more  than  any  other  philosopher,  who  examined  the 
whole  range  of  the  phenomena,  physical  as  well  as 
physiological,  and  whose  work  will  for  generations 
remain  an  enduring  monument  to  his  genius. 


168 


CHAPTER    XIII 

HELMHOLTZ    IN    HEIDELBERG — MINOR  PHYSIOLOGICAL 
RESEARCHES 

IT  must  be  remembered  that,  both  at  Konigs- 
berg  and  Bonn,  Helmholtz  lectured  on  anatomy 
as  well  as  physiology,  and  in  Konigsberg  he  had 
general  pathology  in  addition.  This  makes  it  more 
wonderful,  that  he  should  have  been  able  to  find 
time  for  so  much  physiological  research,  while  it 
explains  his  familiarity  with  human  anatomy.  Even 
in  the  latter  science — a  region  one  would  suppose  so 
harvested  as  not  to  leave  a  straw  for  the  most  indus- 
trious gleaner — he  found  something  to  contribute  to 
human  knowledge. 

In  1856,  his  first  year  in  Bonn,  Helmholtz  com- 
municated two  short  papers  to  the  Medical  Society 
of  the  Lower  Rhine,  both  of  an  anatomico-physio- 
logical  character.  The  first  related  to  the  anatomical 
structure  of  the  thorax.  He  first  showed  that  the 
ribs  are  attached  behind  to  the  vertebrae  and  in  front 
to  the  sternum,  and,  during  a  state  of  rest,  the 
anterior  ends  are  on  a  lower  plane  than  the  posterior. 
When  the  ribs  rise  during  inspiration,  the  sternal 
169 


HERMANN  VON  HELMHOLTZ 

attachment  moves  forwards,  and  thus  the  ribs  and 
their  cartilages  are  submitted  to  torsion.  Thus  each 
rib-ring  has  a  kind  of  elasticity  like  that  of  a  hoop 
lying  on  a  plane  surface,  and  is  stretched  antero-pos- 
teriorly  until  it  is  slightly  oval,  and  the  thorax  may 
be  regarded  as  built  up  of  such  a  series  of  rings.  Each 
ring  is  in  a  position  of  stable  equilibrium,  until  it  is 
submitted  to  the  muscular  effort  of  inspiration,  and 
to  which  it  springs  back  by  its  elasticity.  He  also 
demonstrated  the  greater  mobility  of  the  upper  part 
of  the  chest  in  the  female  than  in  the  male.  Finally, 
he  took  the  view,  that  the  external  intercostals  were 
inspiratory,  while  the  internal  had  more  to  do  with 
abdominal  breathing. 

Somewhat  later  in  the  same  year,  he  lectured  on 
the  muscles  of  the  arm,  and  gave  the  result  of  obser- 
vations made  both  on  the  cadaver  and  on  the  living 
subject.  Most  of  the  actions  described  are  now 
found  in  all  anatomical  books.  He  described  speci- 
ally the  movements  of  the  clavicle  and  scapula.  He 
then  gave  an  account  of  the  possible  movements  of 
the  arm  at  the  shoulder  joint,  supposing  the  arm  to 
be  extended  at  an  angle  of  45°,  with  the  flexor 
surface  directed  forwards.  He  accurately  defined 
three  axes  of  rotation,  one  horizontal  from  before 
backwards,  a  second  parallel  to  the  length  of  the 
upper  arm,  and  a  third  perpendicular  to  the  two 
former.  As  regards  the  process  of  supination  of  the 
170 


HELMHOLTZ  IN  HEIDELBERG 

forearm — that  is,  moving  it  so  as  to  direct  the  palm 
upwards,  he  is  of  opinion  that  the  real  supinator  is 
the  biceps,  and  that  the  so-called  supinator  longus 
is  a  real  flexor.  The  strongest  supination,  when  the 
arm  is  stretched,  is  brought  about  by  the  simultane- 
ous action  of  both  biceps  and  triceps,  and  when  the 
arm  is  flexed,  then  supination  is  brought  about  by 
the  biceps  alone.  The  action  of  the  palmaris  longus 
comes  into  play  when  the  hand  is  made  hollow,  and 
it  appears  to  protect  the  flexor  tendons  from  the 
pressure  of  the  folded  skin.  Finally,  he  showed  that 
in  the  flexed  position,  the  first  phalanges  can  be 
rotated  round  their  own  axis  by  the  interossei 
muscles,  a  movement  which  had  not  previously  been 
observed. 

The  movements  of  the  eyeballs  were  of  great 
interest  to  Helmholtz,  and  he  solved  some  of  the 
difficult  problems  of  single  vision  with  two  eyes.  He 
had,  as  he  himself  remarked,  a  gift  of  seeing  things 
in  their  geometrical  relations,  so  that  he  was  able  to 
deal  with  questions  of  this  nature  with  the  greatest 
ease.  In  the  year  1862,  there  appeared  the  first 
paper  on  the  form  of  the  horopter,  that  imaginary 
field  in  space,  rays  from  any  objects  on  which  must 
fall  on  corresponding  points  of  the  two  retinae,  and 
consequently  give  rise  to  the  sensation  of  a  single 
image.  The  year  1863  saw  two  papers  on  the  move- 
ments of  the  human  eyes,  giving  an  account  of 
171 


HERMANN  VON  HELMHOLTZ 

numerous  ingenious  experiments,  and  containing  a 
mathematical  treatment  of  the  subject.  In  1864,  he 
delivered  the  Croonian  Lecture  to  the  Royal  Society 
— a  famous  lecture — 'On  the  Normal  Motions  of 
the  Human  Eye  in  relation  to  Binocular  Vision,'  and 
this  was  followed  in  the  same  year  by  two  papers 
on  the  horopter.  In  the  following  year,  1865,  he 
published  a  paper  on  the  Influence  of  the  Orienta- 
tion of  the  Eyeballs  on  the  Projection  of  the  Retinal 
Pictures,  another  on  Stereoscopic  Vision,  and  a  third 
on  the  Movements  of  the  Eyeballs.  At  the  Congres 
periodique  internationale  d'Ophtalmologie  a  Paris,  in 
1867,  he  read  a  paper  on  Stereoscopic  Vision  and 
the  Sense  of  Relief.  He  returned  to  the  question  in 
1878,  after  he  became  Professor  of  Natural  Philosophy 
in  Berlin,  and  even  so  late  as  1881,  in  his  sixtieth 
year,  he  published  a  note  in  the  Philosophical  Magazine 
on  the  same  subject. 

It  is  somewhat  difficult  to  give  an  account  of  the 
results  of  those  researches  in  untechnical  language, 
but  it  is  only  fair  to  Helmholtz  to  make  the  attempt. 
A  picture  of  an  external  object  is  formed  on  the 
retina  of  each  eye  by  the  lens-like  structures  placed 
in  front  of  it,  in  accordance  with  the  laws  of  dioptrics. 
The  two  pictures,  however,  give  the  sensation  of  one 
object.  Further,  we  can  move  the  eyeballs  so  as 
to  direct  them  to  the  object  we  wish  to  examine. 
Thus  we  can  move  them  simultaneously  up  to  the 
heavens  or  down  to  the  earth,  or  to  the  right  side 
172 


HELMHOLTZ  IN  HEIDELBERG 

or  to  the  left.  We  can  also  look  straight  onwards, 
as  when  we  gaze  at  the  horizon,  in  which  case  the 
visual  axes  are  parallel ;  or  we  can  look  at  a  nearer 
object,  converging  the  visual  axes  so  as  to  cause 
them  to  meet  at  the  object  under  examination.  The 
effect  of  these  movements  is  always  to  bring  the 
images  upon  corresponding  parts  of  the  two  retinae, 
and  if  they  fall  upon  these,  and  not  upon  others, 
then  there  is  single  vision ;  but  if,  from  various 
causes,  the  images  fall  on  other,  or  non-correspond- 
ing points,  there  will  be  double  vision — that  is  to 
say,  we  shall  see  two  objects  instead  of  one.  The 
pairs  of  points  that  give  rise  to  single  vision  were 
termed  by  Johannes  Miiller  corresponding  points, 
and  the  assumption  was  that  from  any  such  pair  of 
points  similar  nerve-fibres  passed  to  the  brain,  and 
were  possibly  there  so  united  as  to  give  rise  to  the 
consciousness  of  a  single  object. 

Further,  it  has  long  been  known  that  the  retina 
of  each  eye  is  related  to  both  sides  of  the  brain,  or, 
to  put  it  conversely,  each  side  of  the  brain  is  related 
to  both  eyes.  If  the  optic  nerves  are  traced  back- 
wards, they  are  found  to  unite  in  the  well-known 
optic  commissure,  and  from  the  latter  two  great  bands 
of  fibres,  termed  the  optic  tracts,  carry  the  nervous 
impulses  to  the  brain.  The  whole  of  the  nerve-fibres 
from  the  retina  of  each  eye  do  not,  however,  cross  or 
decussate  in  the  commissure  in  the  human  mechan- 
ism, as  was  at  one  time  supposed,  but  they  do  so  in 
173 


HERMANN  VON  HELMHOLTZ 

many  animals,  as,  for  example,  in  the  pigeon.  Thus 
a  pigeon,  in  a  sense,  sees  an  object  on  its  right  side 
with  its  left  brain,  and  vice  versa,  and  as  the  eyeballs 
in  the  bird  are  directed  to  the  sides,  it  probably  sees 
now  with  one  eye,  now  with  the  other,  and  if  objects 
are  immediately  in  front  or  immediately  behind  its 
head,  they  probably  form  indistinct  images,  the  bird 
does  not  see  distinctly,  and  it  therefore  rotates  its  head 
with  a  well-known  pert-like  or  quizzical  action,  so  as 
to  bring  one  eye  to  bear  on  the  object.  In  man,  how- 
ever, and  in  all  the  higher  mammals,  the  decussation 
is  not  complete,  and  the  arrangement  is  probably 
most  complicated  in  man  himself,  so  to  meet  the 
circumstances  of  his  erect  position  with  eyes  in  front, 
looking  straight  out  upon  the  world.  The  fibres 
from  the  nasal  side  of  each  retina  cross  in  the  com- 
missure, while  those  from  the  temporal  sides  keep 
to  their  corresponding  sides.  Thus,  in  the  eyes  of 
a  reader  of  this  page,  the  nerves  from  the  tem- 
poral side  of  the  right  eye  keep  on  the  same  side 
in  their  course  to  the  brain,  but  those  from  the 
nasal  side  cross  over  ;  on  the  other  hand,  the 
nerves  from  the  temporal  side  of  the  left  eye 
also  keep  on  the  same  side,  and  those  from  the 
nasal  side  cross  in  the  commissure.  The  right 
brain  is  thus  related  to  the  temporal  side  of  the 
right  eye  and  to  the  nasal  side  of  the  left,  and 
the  left  brain  is  related  to  the  temporal  side  of  the 
left  brain  and  to  the  nasal  side  of  the  right.  In 


HELMHOLTZ  IN  HEIDELBERG 

this  way  the  effect  is  as  if  the  retinae  were  brought 
together,  and  the  one  were  placed  behind  the  other. 
In  understanding  vision  with  one  eye  there  is  no 
special  difficulty.  The  globe  might  rotate  round  three 
possible  axes,  a  vertical,  a  horizontal,  and  an  antero- 
posterior.  Movements  are  affected  by  four  straight 
muscles  (rect'i)  and  two  oblique.  The  four  straight 
muscles  (rectus  superior,  rectus  inferior,  rectus  externus, 
rectus  internus)  arise  from  the  back  of  the  orbit,  and 
pass  forwards  to  their  insertion  in  the  front  part  of  the 
eyeball,  or  its  equator,  if  we  regard  the  anterior  and 
posterior  ends  of  the  globe  as  the  poles.  The  two 
obliques  (while  one  of  them  also  originates  at  the  back 
of  the  orbit)  come  as  it  were  from  the  nasal  side,  the 
one  goes  above  the  eyeball  and  the  other  below,  and 
both  are  inserted  into  the  eyeball  on  the  temporal  side, 
the  superior  oblique  above,  and  the  inferior  oblique 
below.  The  six  muscles  work  in  pairs.  Thus  the 
internal  and  external  recti  turn  the  eye  round  the 
vertical  axis,  so  that  the  line  of  vision  is  directed  to 
the  right  or  left.  The  superior  and  inferior  recti  turn 
the  eye  round  the  horizontal  axis,  and  thus  the  line 
of  vision  is  raised  or  lowered.  The  oblique  muscles 
turn  the  eye  round  an  axis  passing  through  the  centre 
of  the  eye  to  the  back  of  the  head,  so  that  the  superior 
oblique  lowers  while  the  inferior  oblique  raises  the 
visual  line.  Helmholtz  was  the  first  to  discover  that 
the  oblique  muscles,  in  certain  circumstances,  cause  a 
slight  rotation  of  the  eyeball  round  the  visual  line 
175 


HERMANN  VON  HELMHOLTZ 

itself.  Normally,  the  superior  rectus  co-operates  with 
the  inferior  oblique,  and  the  inferior  rectus  with  the 
superior  oblique. 

The  two  eyeballs  are  also  associated  in  their  move- 
ments in  the  most  exquisite  manner,  an  association 
accomplished  by  a  nervous  mechanism  which  need  not 
here  be  discussed.  Suffice  it  to  say,  that  when  we 
look,  say  to  the  right  side,  the  right  external  and  the 
left  internal  recti  work  together,  and  when  we  look 
towards  the  left  side,  then  there  is  harmonious  co-opera- 
tion between  the  left  external  and  the  right  internal 
recti.  Again,  the  two  superior  recti  act  together  if  we 
look  upwards,  and  the  two  inferior  if  we  look  down- 
wards ;  if  we  look  downwards  pensively  to  the  right 
side,  the  inferior  recti  of  each  eye,  along  with  the 
superior  oblique  on  the  same  side,  and  the  internal 
rectus  on  the  left  side  all  come  into  play  ;  while,  if  we 
look  to  the  left  side,  the  corresponding  muscles  for 
that  movement  are  brought  into  action  ;  and,  finally, 
if  we  look  upwards  and  to  the  right,  then  the  superior 
recti  contract,  and  are  aided  by  the  inferior  oblique  on 
the  right  side,  and  the  internal  rectus  on  the  left  ; 
while,  if  we  assume  the  same  attitude  to  the  left,  the 
superior  recti  again  act,  and  are  assisted  by  the  inferior 
oblique  on  the  same  side,  and  the  internal  rectus  on  the 
right.  As  these  muscles  are  innervated,  in  many  cases, 
from  opposite  sides  of  the  brain,  it  is  clear  that  the 
cerebral  actions  must  be  of  a  very  complicated  char- 
acter. All  these  movements  are  under  the  control  of 
176 


HELMHOLTZ  IN  HEIDELBERG 

the  will,  at  least  up  to  a  certain  point,  but  it  was 
reserved  to  Helmholtz  to  show  that  there  are  other 
and  slighter  movements  that  are  altogether  involun- 
tary. Thus  no  one  can  voluntarily  diverge  the  visual 
lines  ;  in  other  words,  it  is  impossible  voluntarily  to 
cause  simultaneous  contraction  of  both  external  recti. 
Nor  can  we  voluntarily  rotate  the  eyeball  round  the 
antero-posterior  axis,  but  here,  again,  slight  involuntary 
movements  may  be  made.  We  can  thus  turn  the  line 
of  vision  into  every  possible  direction,  but  when  its 
direction  has  been  fixed,  the  position  of  the  eye  is  also 
fixed,  and  is  beyond  our  control. 

Helmholtz  studied  the  subject  by  taking  advantage 
of  the  method  of  Donders,  which,  by  an  ingenious 
device,  he  greatly  improved.  In  this  method,  the 
apparent  position  of  after-images  produced  by  exhaust- 
ing the  retina,  say,  with  a  red  or  green  object,  was 
compared  with  that  of  a  line  or  fixed  point  gazed 
at  with  a  new  position  of  the  eyeball.  The  ocular 
spectra  soon  vanish  in  this  experiment,  but  a  good 
observer  can  determine  with  great  accuracy  the  coin- 
cidence of  lines  with  the  ocular  spectra.  Thus,  after 
producing  an  after-image  with  the  head  in  the  erect 
position,  the  head  may  be  placed  into  any  inclined 
position,  and  if  the  attention  is  then  fixed  :on  vertical 
lines,  it  can  easily  be  seen  whether  the  after-image 
coincides  with  the  lines.  As  the  after-image  must 
remain  in  the  same  position  on  the  retina,  if  it  coin- 
cides with  the  vertical  lines,  it  is  evident  there  must 

M 


HERMANN  VON  HELMHOLTZ 

have  been  a  slight  rotation  of  the  eyeball.  The  coin- 
cidence always  takes  place,  and  thus  it  is  proved  that 
there  is  an  involuntary  rotation.  Helmholtz  also 
showed  that  this  minute  rotation  had  the  advantage  of 
enabling  us  to  judge  more  correctly  than  we  would 
otherwise  do  of  the  position  of  external  objects.  If 
the  eyeball  is  thus  rotated,  the  optic  image  will  be 
slightly  displaced,  but  if  its  new  position  is  parallel  to 
its  former  position,  there  is  no  apparent  motion  ;  but 
if  the  rotation  is  only  through  infinitely  small  angles, 
the  eye  may  move  round  axes  perpendicular  to  the 
visual  line,  and  thus  the  optic  images  will  remain 
parallel  to  their  first  positions.  Now  Listing  had 
already  discovered  the  law  that,  in  the  so-called  third 
positions  of  the  eyeball,  it  rotates,  not  round  an 
antero-posterior  axis,  but  round  axes  perpendicular  to 
the  visual  line.  Helmholtz  demonstrated  the  truth  of 
this  law,  and,  finally,  by  the  calculus  of  variations, 
solved  the  mathematical  problem. 

He  next  proceeded  to  investigate  single  vision  with 
both  eyes.  The  two  fields  of  view  that  seem  to  be 
superposed  are  the  corresponding  or  identical  points  of 
Johannes  Miiller.  But  we  see  things  in  relief;  this 
may  also  be  done  with  Wheatstone's  stereoscope,  and 
in  neither  case  can  we  perceive  the  duplicity  of  the 
images.  Helmholtz  showed,  however,  that  if  we  sup- 
pose two  objects,  say  two  stereoscopic  pictures,  to  have 
vertical  lines  or  meridians  that  are  not  in  reality  truly 
vertical,  but  each  set  slightly  inclined  to  the  right  or 
178 


HELMHOLTZ  IN  HEIDELBERG 

left,  and  if  we  look  at  these  through  a  stereoscope,  the 
'squinting'  lines  accurately  coincide,  thus  showing 
that  in  double  vision  it  is  not  the  real  vertical  meridians 
of  the  fields  of  view  that  coincide,  but  the  apparently- 
vertical  meridians.  The  horizontal  meridians  always 
coincide.  Thus  while  the  retinal  horizon  is  horizontal 
for  both  eyes,  the  apparently  vertical  meridians  are  not 
perpendicular  to  it,  as  had  been  hitherto  supposed,  but 
they  diverge  at  their  upper  extremity,  at  an  angle  of 
from  2°  22'  to  2°  33'.  Corresponding  points  are 
therefore  equally  distant  from  each  retinal  horizon, 
and  from  each  apparently  vertical  meridian.  This 
led  to  the  examination  of  the  true  geometrical  form 
of  the  horopter,  by  which  is  meant  the  locus  of 
those  points  of  space  which  are  projected  on  cor- 
responding retinal  points,  and  he  found  that  it  is 
generally  a  line  of  double  curvature  produced  by  the 
intersection  of  two  hyperboloids,  that  is  to  say,  it  is 
a  twisted  cubic  curve  formed  by  the  intersection  of 
two  hyperboloids  which  have  a  common  generator, 
and  in  some  special  cases  it  is  a  combination  of  two 
plane  curves.1  The  curves  pass  through  the  nodal 
points  of  both  eyes.  An  infinite  number  of  lines 
may  be  drawn  from  any  point  of  the  horopter  so  as 
to  be  seen  single,  and  these  lines  lie  on  a  cone  of  the 
second  order  whose  vertex  is  the  point.  Helmholtz 
also  showed  that  when  we  look  at  the  horizon,  the 

1  The    mathematical  demonstration   is  given   in    Heat/is  Geometrical 
Optics,  p.  233.     Cambridge,  1887. 

179 


HERMANN  VON  HELMHOLTZ 

horopter  is  really  a  horizontal  plane  passing  through 
our  feet,  thus  warranting  the  name  first  given  to  it  by 
Aguilonius  in  1613.  The  horopter  in  this  case  is  the 
ground  on  which  we  stand.  Experiments  show 
1  that  the  forms  and  the  distances  of  these  objects 
which  are  situated  in,  or  very  nearly  in,  the  horopter, 
are  perceived  with  a  greater  degree  of  accuracy  than 
the  same  forms  and  distances  would  be  when  not  situ- 
ated in  the  horopter.' 

The  investigation  of  this  subject  led  Helmholtz  to 
the  invention  of  the  telestereoscope,  an  instrument 
containing  a  combination  of  prisms,  by  which  two 
images  of  distant  objects  can  be  seen  as  if  the  eyes 
were  widely  separated  in  the  head.  Consequently, 
combination  takes  place,  and  the  objects  are  seen  in 
relief.  Further,  Helmholtz,  in  his  later  researches, 
came  to  the  conclusion,  that  the  apparent  fusion 
of  two  retinal  images  cannot  be  explained  by 
any  anatomical  arrangement,  but  that  it  is  due 
to  a  mental  act.  Briicke's  notion,  that  the  per- 
ception of  solidity  might  be  due  to  sensations  excited 
by  muscular  contractions  causing  convergence  of  the 
visual  axes,  is  negatived  by  Dove's  observation, 
that  the  illusion  of  stereoscopic  pictures  is  also  pro- 
duced when  they  are  illuminated  by  the  electric 
spark,  lasting  less  than  the  f^fth  of  a  second, 
and  in  'this  short  time  there  cannot  be  the 
slightest  movement  of  the  eyeballs.  The  study  of 

stereoscopic  lustre,  also  first  noticed   by  Dove,  pro- 
180 


HELMHOLTZ  IN  HEIDELBERG 

duced  when  one  stereoscopic  picture  is  white  and  the 
other  grey,  shows  also  that  the  impressions  on  the  two 
retinas  are  not  combined,  in  this  case,  into  one  sensa- 
tion. There  is  a  rivalry  of  the  fields  of  visions,  best 
seen  in  the  rivalry  of  colours,  when  one  stereoscopic 
picture  is  red  and  the  other  blue.  A  true  combina- 
tion purple  is  not  produced,  but  there  is  a  peculiar 
'sheen,'  and  the  red  at  one  moment  has  the  pre- 
dominance, and  the  instant  after  it  is  the  blue. 

The  whole  of  this  beautiful  research  is  a  good 
illustration  of  the  method  of  Helmholtz.  Complicated 
as  the  movements  of  the  eyeball  apparently  are,  they 
become  simple  when  we  consider  that  they  are  just 
the  movements  that  are  necessary  to  see  single  objects 
with  two  eyes.  It  was  this  simple  principle  that 
guided  Helmholtz.  Only  those,  however,  who  have 
read  the  chapters  on  the  subject  in  his  Physiological 
Optics  can  form  a  conception  of  the  amount  of  work 
expended  upon  it.  The  bibliography  alone  is  a  model 
of  literary  research. 

In  1869,  he  investigated  the  cause  of  hay-fever,  a 
troublesome  affection  to  which  he  was  susceptible, 
and  which  interfered  much  with  his  pleasure  during 
holiday  time.  He  announced  the  discovery  in  a  letter 
to  Binz,  who  secured  its  insertion  in  Virchow's  Archiv 
fur  pathologische  Anatomie.  Helmholtz  found  in  the 
mucus  of  the  nasal  secretions  of  persons  affected  by 
this  disease  micro-organisms  of  a  vegetable  nature, 
181 


HERMANN  VON  HELMHOLTZ 

and  having  observed  the  researches  of  Binz  on  the 
poisonous  action  of  sulphate  of  quinine  on  such  organ- 
isms, he  applied  to  the  mucous  membrane  of  the 
nostrils  a  solution  of  one  of  the  salt  in  eight  hundred 
of  water,  with  almost  instant  relief.  This  thera- 
peutical measure  was  first  carried  out  in  1867  ;  it 
was  often  repeated,  and,  in  1872,  Helmholtz  told  Binz 
that  he  was  quite  cured.  To  medical  men  Helmholtz's 
descriptions  of  the  disease  will  be  interesting,  and 
possibly  it  shows  that  he  might  have  made  an  excellent 
clinical  observer.1 

'An  extraordinary  violent  sneezing  then  sets  in, 
and  a  strongly  corrosive  thin  discharge,  with  which 
much  epithelium  is  thrown  off.  This  increases,  after 
a  few  hours,  to  a  painful  inflammation  of  the  mucous 
membrane  and  of  the  outside  of  the  nose,  and  excites 
fever,  with  severe  headache  and  great  depression,  if  the 
patient  cannot  withdraw  himself  from  the  heat  and  the 
sunshine.  In  a  cool  room,  however,  these  symptoms 
vanish  as  quickly  as  they  come  on,  and  there  then  only 
remains  for  a  few  days  a  lessened  discharge  and  soreness, 
as  if  caused  by  the  loss  of  epithelium.  I  remark, 
by  the  way,  that  in  all  my  other  years  I  had  very 
little  tendency  to  catarrh  or  catching  cold,  while 
the  hay-fever  has  never  failed,  during  the  twenty-one 
years  of  which  I  have  spoken,  and  has  never  attacked 
me  earlier  or  later  in  the  year  than  the  time  named.' 

1  Nature,  vol.  x.,  p.  26,  May  4,  1874.  Letter  to  Prof.  Tyndall  from 
Prof.  Binz  of  Bonn. 

182 


CHAPTER    XIV 

HELMHOLTZ  IN  BERLIN PHYSICAL  RESEARCHES 

HELMHOLTZ  occupied  the  Chair  of  Physiology 
in  Heidelberg  from  1859  to  1871,  when  he 
was  placed  in  the  chair  of  Magnus  in  Berlin.  In 
Heidelberg  he  lectured  upon  physiology  only,  and  he 
had  thus  greater  leisure  to  devote  to  physical  and 
physiological  research.  During  this  period  of  eleven 
years,  he  contributed  nearly  sixty  papers,  and,  of  these, 
twenty-four  were  on  physical  questions.  Even  this 
statement,  however,  does  not  give  full  expression  to 
his  intellectual  activity,  for  the  great  work  on  Physio- 
logical Optics  made  its  appearance  in  parts  in  1856, 
1860,  and  1867,  and  the  equally  valuable  book  on 
Sensations  of  Tone  was  published  in  1863,  both  books 
full  of  the  results  of  special  research.  He  also  lectured 
at  the  Royal  Institution  of  Great  Britain  on  the 
Conservation  of  Energy  in  1864,  and,  from  time  to 
time,  he  delivered,  and  in  1865  and  1871  published, 
some  of  those  admirable  popular  lectures  that  represent 
the  highest  class  of  that  form  of  literature  in  any 
language. 

'83 


HERMANN  VON  HELMHOLTZ 

Indeed,  it  may  be  said  that  this  was  a  transitional 
period  in  the  life  of  Helmholtz.  A  born  physicist,  as 
he  himself  often  said,  he  more  and  more  occupied  his 
mind  with  some  of  the  deepest  problems  in  this  depart- 
ment of  science.  From  1866,  when  he  published  a 
well-known  paper  on  the  sounds  emitted  by  a  contract- 
ing muscle,  and  1867,  when  the  elaborate  investiga- 
tion of  the  bones  of  the  ear  appeared,  he  published  little 
that  was  purely  physiological,  and  he  devoted  himself 
almost  entirely  to  physics.  As  he  felt  that  this  was 
his  vocation,  he  left  physiological  research  to  a  great 
extent  in  the  hands  of  pupils,  assisting  and  counselling 
them  in  their  work,  sometimes  co-operating  in  publica- 
tion, as  when,  in  1867  and  1870,  he  issued  the  results 
of  a  research  by  himself  and  his  pupil  Baxt  on  the 
velocity  of  the  nervous  impulse  in  the  motor  nerves 
of  man. 

On  the  death  of  Magnus  in  1871,  it  was  felt  that 
only  one  of  two  men  in  Germany  could  take  his  place 
as  Professor  of  Physics  in  the  University  of  Berlin. 
Du  Bois  Reymond,  who  was  then  Rector  of  the 
University,  was  empowered  by  von  Miiller,  the 
Minister  of  Education,  to  go  to  Heidelberg  and 
persuade  Kirchhoff,  one  of  the  founders  of  spectrum 
analysis,  or  Helmholtz,  to  accept  the  vacant  chair. 
The  Government  of  Baden  would  not  allow  Kirchhoff 
to  leave,  and  so  the  chair  was  offered  to  Helmholtz. 
This  he  accepted  with  some  reluctance,  for  he  loved 
the  wooded  hills  around  Heidelberg  and  the  old 
184 


HELMHOLTZ  IN  BERLIN 

romantic  town,  but  no  doubt  also  he  yielded  to  the 
entreaty  of  his  friend  with  pride  and  satisfaction. 
He  had  now  raised  himself  to  the  position  of  being 
the  first  physicist  in  Germany,  and  his  fame  extended 
throughout  the  scientific  world.  The  young  army 
surgeon,  who  astonished  his  friends  twenty-four  years 
before  by  writing  the  c  tract ' I  (as  it  is  modestly  called 
by  himself  and  by  Clerk  Maxwell),  was  now,  at  the 
age  of  fifty,  in  a  position  where  he  could  give  his 
undivided  attention  to  his  first  love — physical  science 
— a  position,  also,  specially  suited  to  his  inclination 
and  talent. 

The  years  rolled  on  till  1887,  when  another  great 
change  took  place  in  the  career  of  Helmholtz.  His 
life-long  friend,  Werner  von  Siemens,  the  electrician 
and  man  of  affairs,  founded  a  great  Physico-Technical 
Institute  at  Charlottenburg,  near  Berlin,  and  Helm- 
holtz was  chosen  as  its  first  director.  The  object 
of  this  institute  was  (i)  to  deal  with  costly  and  diffi- 
cult scientific  investigations  not  likely  to  be  under- 
taken in  any  ordinary  physical  laboratory,  such  as 
those  relating  to  standards  of  measurement ;  and 
(2)  to  undertake  special  technical  procedures,  includ- 
ing the  testing  of  all  kinds  of  thermometers,  con- 
structed on  the  most  approved  principles,  the  testing 
of  aneroids,  mercurial  barometers,  the  examination  of 
all  kinds  of  instruments  for  electrical  measurements, 
the  examination  of  photometric  instruments,  and  the 

1  Die  Erhahung  der  Kraft ;   or,  The  Conservation  of  Energy. 
I85 


HERMANN  VON  HELMHOLTZ 

establishment  of  a  unit  of  light ;  the  testing  of  tuning 
forks,  the  construction  of  universal  screws,  and,  in- 
deed, all  methods  and  instruments  having  to  do  with 
higher  technical  research  and  instruction.  The  In- 
stitution had  at  least  one  point  of  contact  with  the 
medical  profession,  as  we  find  that  25,000  clinical 
thermometers  were  tested  and  stamped  during  the 
first  three  years. 

Werner  von  Siemens,  whose  admiration  for  the 
talents  of  his  friend  was  boundless,  wished  Helmholtz 
to  be  entirely  relieved  from  teaching,  so  as  to  leave 
his  energies  freedom  to  work  in  the  higher  regions  of 
research,  but  circumstances  made  it  important  that 
Helmholtz  should  retain  his  chair.  This  he  did  till  the 
year  of  his  death  in  1894,  lecturing  during  the  session 
twice  a  week  on  such  special  subjects  as  the  mathe- 
matical theory  of  vibrations,  electrodynamics,  and  the 
mathematical  developments  of  light  and  sound.  In 
the  Institute,  with  a  staff  of  fifty  officials,  Helmholtz 
had  now  to  undertake  much  administrative  work,  and 
he  performed  this  part  of  his  duties  with  the  same 
zeal  and  thoroughness  that  had  characterised  his  whole 
life.  It  was  certainly  work  different  from  that  to 
which  he  had  been  accustomed,  far  removed,  for 
example,  from  the  fascinating  study  of  sense-percep- 
tions, but  it  was  public  work  to  which  Helmholtz 
attached  great  importance.  His  mind  still  soared  into 
the  loftiest  regions  of  scientific  thought,  and  some  of 
his  most  advanced  papers  on  mathematical  physics 
186 


HELMHOLTZ  IN  BERLIN 

appeared  during  the  last  ten  years  of  his  busy  life. 
Further,  he  was  cheered  by  the  social  brightness  of  a 
happy  home  life.  In  1861,  Helmholtz  entered  upon 
a  second  marriage  with  Miss  Anna  von  Mohl,  of  a 
Wiirtemberg  family  of  high  social  position.  This 
lady  became  the  worthy  helpmate  of  so  great  a  man  ; 
by  her  side  many  of  his  immortal  works  were  created, 
and  their  home  was  the  centre  of  a  brilliant  social, 
artistic,  and  intellectual  circle.  Two  children  were 
born  of  this  marriage.  The  elder  son,  Robert,  died 
in  1889  at  a  comparatively  early  age,  after  he  had 
given  promise  of  having  inherited  some  of  the  apti- 
tude for  mathematical  and  physical  research  which 
so  distinguished  his  father  ;  while  the  daughter  knit 
together  the  houses  of  Siemens  and  Helmholtz  by 
marrying  the  son  of  Werner  von  Siemens.  The  loss 
of  his  son  was  deeply  felt,  and  it  is  said  that  Helm- 
holtz never  recovered  from  the  blow.  Thus  the 
brilliancy  of  his  career  was  dimmed  by  his  experience 
of  sad  events  that  come  to  all  alike. 

During  the  last  twenty-three  years  of  his  life,  Helm- 
holtz devoted  his  energies  entirely  to  the  investigation 
of  physical  problems.  The  only  exception  to  this 
statement  is,  that  questions  of  a  philosophical  nature, 
which  will  be  dealt  with  in  a  future  chapter,  also 
engaged  his  attention.  To  these  questions  he  was 
led  by  the  consideration  of  his  theory  of  knowledge, 
founded  on  the  thorough  examination  he  had  made 
into  the  nature  of  sensation  and  perception.  In 
187 


HERMANN  VON  HELMHOLTZ 

physical  science  he  occupied  himself  almost  wholly 
with  profound  discussions,  of  a  highly  mathematical 
character,  into  hydrodynamics,  or  the  motions  of 
fluids,  whether  liquid  or  aeriform  ;  into  the  nature  of 
the  ether  and  its  relations  to  electrodynamics  and 
thermodynamics ;  into  some  of  the  phenomena  of 
light ;  and  into  principles  concerned  in  the  move- 
ments of  atoms  and  lying  at  the  root  of  mechanics. 
He  also  applied  his  profound  knowledge  of  the  more 
hidden  physical  movements  to  an  explanation  of 
chemical  phenomena,  more  especially  as  to  the  rela- 
tion of  these  phenomena  to  the  law  of  the  conser- 
vation of  energy ;  and,  finally,  he  passed  into  the 
region  of  the  physics  of  certain  meteorological  pheno- 
mena, such  as  the  nature  of  clouds.  It  is  remarkable, 
as  showing  the  vigour  of  his  intellect,  that  he  was 
creative  up  to  the  year  of  his  death.  Year  after 
year  he  ventured  higher  and  higher  in  the  choice  of 
problems  on  which  to  exercise  his  powers,  and 
although  he  gave  the  results  in  his  ordinary  lectures, 
the  number  of  pupils,  and  indeed  of  physicists, 
throughout  the  world,  who  could  follow  him,  became 
fewer  and  fewer. 

Helmholtz  had  transcendent  gifts  as  a  mathema- 
tician. We  have  it  on  the  authority  of  Du  Bois 
Reymond,  that  not  long  before  he  wrote  the  tract 
on  the  conservation  of  energy,  his  younger  friends 
were  astonished  at  his  mathematical  attainments  and 
at  the  width  of  his  reading  of  the  more  famous 
188 


HELMHOLTZ  IN  BERLIN 

mathematical  treatises.  Had  he  chosen  pure  mathe- 
matics as  his  future  field  of  labour,  there  is  no  doubt 
he  would  have  won  distinction  here  as  elsewhere,  but 
he  always  subordinated  mathematics  to  the  investi- 
gation of  physical  questions.  He  did  not  revel  in  the 
deduction  of  the  purely  abstract  truth  of  geometry 
and  algebra,  but  the  abstract  propositions  and  methods 
of  mathematics  were  to  him  a  means  to  an  end,  and 
he  knew  that  mathematical  analysis  is  only  a  rigid 
system  of  logic  in  which  wrong  premises  may  conduct 
more  surely  to  a  wrong  conclusion.  He  therefore 
always  endeavoured,  if  possible,  to  obtain  data  on 
which  to  base  his  calculations.  Yet  no  one  knew 
better  that  mathematics  will  win  victories  where 
experiment  may  be  beaten,  and  that,  to  use  the 
words  of  Lovering,  '  mathematical  analysis,  with  its 
multitudinous  adaptations,  is  the  only  key  which  will 
fit  the  most  intricate  wards  of  the  lock  guarding 
the  treasury  of  science.'  Thus,  in  a  review  of  Vol. 
I.  of  Lord  Rayleigh's  Theory  of  SoundJ  Helmholtz 
remarks  :  '  Without  the  resources  of  mathematics,  a 
really  complete  insight  into  the  casual  connection  of 
the  phenomena  of  acoustics  is  altogether  impossible.' 
Again,  he  says :  '  We  see  in  mathematics  the  logical 
activity  of  our  mind  in  its  purest  and  most  perfect 
form,  and  while  we  are  conscious  of  the  toil  and  of 
the  difficulty  in  forming  abstract  ideas,  we  have  at 
the  same  time  confidence  in  the  security,  influence, 

1  Nature^  vol.  xvii.,  p.  238. 
189 


HERMANN  VON  HELMHOLTZ 

and  fruitfulness  of  such  mental  labour.'  The  same 
is  true  of  all  departments  of  physics,  and  especially 
of  those  departments  that  deal  with  the  hidden  pro- 
perties of  matter.  It  need  scarcely  be  said  that  the 
pure  mathematicians,  men  always  of  the  first  mental 
calibre,  are  forging  the  tools  with  which  the  physicists 
of  the  future  will  attempt  to  solve  still  more  recondite 
problems  than  those  that  at  present  engage  their  atten- 
tion. When  the  monumental  labours  of  such  men 
as  William  Rowan  Hamilton,  Joseph  Sylvester,  and 
Arthur  Cayley  are  looked  at  from  this  point  of  view, 
it  will  be  seen  that  advanced  mathematics  does  not 
consist  merely  of  a  series  of  mental  gymnastics,  but 
that  the  subject  is  of  the  highest  practical  importance, 
because  it  leads  the  way  to  an  adequate  conception 
of  the  phenomena  in  the  physical  universe. 


O  wretched  race  of  men,  to  space  confined  ! 
What  honour  shall  you  pay  to  him  whose  mind 

To  that  which  lies  beyond  hath  penetrated  ? 
The  symbols  he  hath  formed  shall  sound  his  praise, 
And  lead  him  on  to  unimagined  ways, 

To  conquests  new  in  worlds  not  yet  created.' 1 


It  may  be  said,  in  the  words  of  Helmholtz's  greatest 
pupil,  Heinrich  Hertz,  that  the  ultimate  function  of 
science  is  to  formulate  the  problems  of  nature  mathe- 
matically, and  thus  bring  the  logical  consequences  of 
thought  into  harmony  with  the  phenomena  happening, 

1  Lines  written  by  Clerk  Maxwell  with  reference  to  Cayley. 
I90 


HELMHOLTZ  IN  BERLIN 

or  appearing  to  happen,  in  the  outer  world.  When 
this  has  been  accomplished,  then  all  physical  problems 
will  be  solved.  Even  now  the  mind  can  imagine 
such  a  being  as  arose  to  the  mental  vision  of  Laplace, 
thus  described  by  Helmholtz  himself:  'An  intelli- 
gence which  at  any  given  instant  should  know  all 
the  forces  by  which  nature  is  urged,  and  the  respec- 
tive situation  of  the  beings  of  which  nature  is  com- 
posed ;  if,  moreover,  such  a  mind  were  sufficiently 
comprehensive  to  subject  these  data  to  calculation, 
such  an  intelligence  would  include  in  the  same  for- 
mula the  movements  of  the  largest  bodies  of  the 
universe  and  those  of  the  smallest  atoms.  Nothing 
would  be  uncertain  to  such  an  intelligence,  and  the 
future  no  less  than  the  past  would  be  present  to 
his  eyes/ 

G.  H.  Wiedemann,1  a  contemporary  of  Helmholtz, 
aptly  points  out  that  he  had  two  methods  of  looking 
at  things,  which  he  used  according  to  the  nature  of 
the  problems  treated  and  their  state  of  development. 
( i )  In  his  earlier  works,  and  in  a  few  of  the  later 
ones,  Helmholtz  starts  from  general  principles  of 
dynamics,  or  from  general  differential  equations, 
and  attains  results  without  special  assumptions  as  to 
the  structure  of  matter,  or  the  nature  of  electricity. 
Examples  of  this  method  are  afforded  by  the  tract 
on  the  conservation  of  energy,  by  his  examination 

1  Introduction  to  Helmholtz's  Witsenschaftliche  Abhandlungen^  vol. 
Hi.  Leipzig,  1895. 


HERMANN  VON  HELMHOLTZ 

of  Weber's  statement  of  electrical  action  at  a  distance, 
and  by  his  papers  on  hydrodynamics  ;  (2)  later  works, 
such  as  those  on  electrolysis  and  on  the  more  hidden 
movements  implied  in  his  theory  of  cyclic  systems, 
show  Helmholtz  taking  advantage  of  molecular  hy- 
potheses. In  his  appreciation  of  Helmholtz's  labours, 
Wiedemann  gives  this  little  personal  touch  to  the 
picture  that  seems  to  bring  the  man  before  us :  c  Helm- 
holtz did  with  nature  just  what  he  did  in  looking  at  a 
picture  or  listening  to  a  piece  of  music.  He  looked 
for  a  scientific  foundation  and  analysed  his  feelings. 
The  waves  of  the  sea  breaking  on  Cape  d'Antibes 
roused  his  scientific  spirit.  From  the  relative  velocity 
of  the  wind  and  the  number  of  waves  on  the  surface 
of  the  sea,  he  drew  conclusions  as  to  the  arrangement 
of  the  clouds,  and  these  were  submitted  to  mathe- 
matical investigation.1 

An  exhaustive  account  of  the  physical  researches  of 
Helmholtz  would  far  exceed  the  limits  of  this  work  ; 
and  indeed  it  is  almost  impossible  to  give  the  results 
in  untechnical  phraseology  without  running  the  risk 
of  being  much  misunderstood,  and  yet  no  true  notion 
can  be  formed  of  this  great  Master  in  Medicine  without 
recognising  that  it  was  in  physical  research,  both  in 
the  animate  and  inanimate  world,  that  he  truly  ex- 
celled. In  this  department  the  labours  of  his  life  may 
be  summed  up  under  six  heads:  (i)  On  the  Con- 
servation of  Energy  ;  (2)  On  Hydrodynamics  ;  (3)  On 

1  Wiedemann,  op.  cit.  xzxi. 
I92 


HELMHOLTZ  IN  BERLIN 

Electrodynamics  and  Theories  of  Electricity ;  (4) 
On  Meteorological  Physics  ;  (5)  On  Optics  ;  and  (6) 
On  the  Principles  of  Dynamics. 


I.   On  the  Conservation  of  Energy. 

This  has  already  been  dealt  with  in  Chapter  V.,  and 
it  has  been  shown  that  Helmholtz  played  an  important 
part  in  formulating,  from  a  mathematical  standpoint, 
this  great  principle.1  In  the  labours  of  his  after 
life  it  was  his  guiding  star.  It  pointed  out  the  path 
of  research,  while  it  was  the  final  test  to  which  all 
theories  were  submitted.  The  tract  not  only  estab- 
lished the  theory  from  general  principles,  but  it  con- 
tained illustrations  of  an  electrical  character  to  which 
reference  is  still  made  in  all  discussions  of  the  subject.2 
In  later  researches  he  verified  Lord  Kelvin's  doctrine 
of  the  dissipation  of  energy  that  only  certain  forms  of 
energy  can  be  completely  changed  into  others — a 
result  in  accordance  with  the  second  law  of  thermo- 
dynamics, which  asserts  that  it  is  impossible,  by  the 
unaided  action  of  natural  processes,  to  transform  any 
part  of  the  heat  of  a  body  into  mechanical  work, 
except  by  allowing  heat  to  pass  from  that  body  into 
another  at  a  lower  temperature.3  This  is  the  modern 

1  See  Tait's  Sketch  of  Thermo-dynamics,  p.  68.      Edinburgh,  1877. 

2  Clerk  Maxwell.      Electricity  and  Magnetism,  vol.  ii.,  p.  176.     Ox- 
ford, 1873. 

3  Clerk  Maxwell.     Theory  of  Heat,  p.  153.     London,  1872. 

N 


HERMANN  VON  HELMHOLTZ 

basis  of  Carnot's  principle,  and  was  first  given  in  a 
somewhat  less  definite  form  by  Clausius,  who  pub- 
lished his  work  soon  after  he  had  reported  to  the 
Physical  Society  of  Berlin  on  Helmholtz's  paper  on 
the  Conservation  of  Energy.  Helmholtz,  in  1883, 
also  applied  the  principle  to  chemical  phenomena.1 
Starting  from  the  fact  that  heat  never  passes  from 
a  colder  to  a  warmer  body  without  making  the 
former  colder  and  the  latter  warmer,  and  that  all 
the  energy  which  already  exists  as  heat  cannot  be 
converted  into  visible  external  energy,  he  drew  a 
great  distinction  between  free  and  restricted  energy. 
Thus  the  energy  of  the  chemical  changes  in  a  galvanic 
element  cannot,  without  further  chemical  changes, 
become  a  measure  of  the  electro-motive  force  ;  only 
a  small  part  of  the  energy  appearing  as  electrical 
energy.  In  all  chemical  changes  in  which  heat 
appears,  all  the  energy  does  not  appear  as  heat,  but 
a  portion  is  still  locked  up  in  the  chemical  compounds. 
Thus  the  internal  energy  of  a  system  may  be  said  to  be 
composed  of  free  and  restricted  energy,  of  which  the 
former  can  be  changed  into  work  while  the  second 
appears  as  heat.  He  thus  gives  us  a  glimpse  into  the 
dynamics  of  chemical  processes,  and  especially  those  of 
dissociation. 

2.   On  Hydrodynamics. 
Helmholtz  published  eight  important  papers  on  the 

1  WitfenschaftL  Abhandlungen,  Bd.  iii.,  s.  92. 
194 


HELMHOLTZ  IN  BERLIN 

movements  of  fluids.  It  was  in  1858,  while  he  was 
Professor  of  Physiology  in  Bonn,  that  he  published  his 
famous  paper  on  Vortex  Motion.1  The  paper  was 
adversely  criticised  by  the  French  mathematician 
Bertrand  ;  and,  in  1868,  Helmholtz  replied  in  such 
a  manner  as  to  silence  controversy,  in  three  papers 
published  in  the  Comptes  Rendus  de  V Academic  des 
Sciences  de  Paris.  In  the  same  year  appeared  a  valu- 
able paper  on  the  discontinuous  motion  of  fluids  ; 
in  the  following  year,  one  on  stationary  streams ; 
and,  in  1873,  an  important  theoretical  paper,  in 
which  is  developed  a  theorem  with  respect  to  geo- 
metrically similar  movements  of  fluid  bodies,  and  their 
application  to  the  mechanical  problem  of  steering 
balloons.  There  are  also  remarks  on  the  mechanism 
of  flight.  Undoubtedly  the  most  important  of  these 
contributions  to  science  is  that  on  vortex  motion, 
an  investigation  that  had  baffled  such  great  mathe- 
maticians as  Euler  and  Lagrange,  on  account  of 
inherent  difficulties.  Stokes  first  pointed  out  the 
real  distinction  between  vortex  and  non-vortex 
motion  ;  but  it  was  reserved  for  Helmholtz  to  dis- 
cover the  fundamental  laws  which  govern  vortex 
motion. 

A  fluid  differs  from  a  solid  body  in  that  its  particles, 
within  certain  limits,  can  move  relatively  to  one 
another.  Practically,  even  in  the  most  mobile  or 
least  viscous  of  fluids,  relative  motion  of  contiguous 

1  Wissenschaftl.  Abhandlungen,  Bd.  i.,  s.  101. 


HERMANN  VON  HELMHOLTZ 

parts  is  more  or  less  gradually  destroyed  by  virtue  of 
viscosity  or  fluid  friction.  In  a  viscid  fluid  there  is 
a  great  internal  friction  ;  and  from  this  extreme  case 
we  can  pass  by  gradations  to  fluids  of  less  viscosity 
until  we  arrive  at  a  very  mobile  fluid  like  sulphuric 
ether.  This  suggests  the  abstraction  of  a  perfectly 
frictionless  fluid,  in  which  there  is  no  tangential  stress 
between  elements  sliding  past  one  another.  The 
greater  part  of  the  theory  of  hydrodynamics  deals  with 
such  an  ideal  fluid,  for  the  simple  reason  that  our 
mathematical  methods  are  insufficient  to  attack  the 
general  problem  of  the  motion  of  a  viscous  fluid.  Al- 
though no  known  fluid  is  even  approximately  friction- 
less,  nevertheless  the  study  of  the  ideal  frictionless  fluid 
leads  to  important  results  and  must  ultimately  enable 
us  to  understand  better  the  effects  of  fluid  friction. 
In  1858  Helmholtz  investigated,  mathematically,  the 
laws  of  vortex  motion  in  a  frictionless  fluid.  In 
addition  to  the  very  remarkable  theorems  in  hydro- 
dynamics, to  which  Helmholtz  was  led  and  on  which 
Lord  Kelvin  and  others  have  based  whole  theories  of 
the  ultimate  constitution  of  matter,  the  investigation 
has  another  important  side.  The  mathematical  for- 
mulae are  identical  with  certain  formulae  in  electro- 
magnetism,  so  that,  as  Helmholtz  himself  pointed  out, 
there  is  a  striking  analogy  between  the  two  apparently 
distinct  classes  of  phenomena,  hydrokinetics  and  electro- 
kinetics. Indeed  all  mechanical  models  that  aim  at 
explaining  the  reciprocal  relations  of  electricity  and 
196 


HELMHOLTZ  IN  BERLIN 

magnetism  require  rotating  elements  ;  and  vorticity  of 
some  kind  seems  to  be  an  essential  feature  of  electro- 
magnetic action. 

Wherever  in  a  fluid  vortex  motion  exists,  there  is 
rotation  of  the  smallest  imaginable  particle  about  some 
axis.  Starting  from  this  conception,  which  Stokes  was 
the  first  to  describe  clearly,  Helmholtz  proceeds  to 
investigate  the  forms  and  behaviour  of  vortices.  A 
vortex  line  he  defines  as  a  line  drawn  through  the 
fluid  in  such  a  way  that  its  direction  at  any  point  is 
the  axis  of  rotation  of  the  element  at  that  point.  A 
vortex  filament  is  part  of  the  fluid  marked  off  from 
the  surrounding  fluid  by  drawing  the  corresponding 
vortex  lines  through  all  points  of  the  circumference  of 
an  infinitely  small  plain  area.  Thus  each  vortex 
filament  may  be  imagined  to  be  shut  off  from  the 
surrounding  fluid  by  a  thin  layer  or  mantle  of  vortex 
lines.  Vortex  lines  form  closed  curves  in  a  finite 
fluid  ;  and  vortex  filaments  form  closed  filaments  or 
rings,  simple  or  knotted.  The  simplest  type  of  a 
vortex  ring  is  a  circular  anchor  ring,  every  element 
rotating  round  the  circular  axis.  Such  a  vortex  ring 
advances  through  the  fluid  in  the  direction  of  motion 
of  the  elements  on  the  inside  of  the  ring.  An  ordinary 
smoke-ring  shows  the  essential  nature  of  the  motion 
very  well.  If  two  vortex  rings  have  the  same  axis 
and  the  same  sense  of  rotation,  and  if  they  both 
advance  through  the  fluid  in  the  same  direction, 
the  first  ring,  a,  will  widen,  and  suffer  retardation, 
197 


HERMANN  VON  HELMHOLTZ 

and  the  second,  £,  will  become  narrower,  and  suffer 
acceleration,  b  ultimately  overtaking  a,  and,  under 
favourable  conditions,  passing  through  it.  Then  they 
will  separate  and  again  follow  each  other,  but  b  will 
widen,  and  a  contract,  until  a  will  pass  through  b. 
Thus  the  vortex  rings  will  pass  alternately  through 
each  other.  On  the  other  hand,  if  the  coaxial  rings 
have  equal  radii  and  equal  rotational  movements,  but 
in  opposite  senses,  they  will  approach  each  other 
and  suffer  distension,  and  this  mutual  approach  and 
simultaneous  spreading  out  will  go  on  indefinitely 
until  the  rings  are  infinitely  close  and  infinitely 
wide. 

In  an  incompressible  frictionless  fluid  rotatory 
movements  can  neither  originate  nor  disappear  ;  the 
vorticity,  or  product  of  any  section  of  the  ring  and 
the  speed  of  rotation,  then  is  an  unchangeable 
quantity.  As  they  move  in  the  surrounding  fluid 
they  are  always  composed  of  the  same  particles. 
Thus  the  vortex  rings  have  perpetuity.  They  may 
jostle  against  each  other  and  undergo  endless 
changes  of  form,  but  they  cannot  be  broken  or 
dissolved.  They  have  the  indestructibility  which  is 
believed  to  belong  to  the  ultimate  constituents  of 
matter.  Lord  Kelvin  made  Helmholtz's  investi- 
gation the  basis  of  the  splendid  hypothesis,  that  the 
atoms  of  matter  are  composed  of  minute  vortex 
rings  in  the  ether,  and  he  worked  out  in  detail 
the  analogy  between  such  rotational  movements  and 
198 


HELMHOLTZ  IN  BERLIN 

electro-magnetic  phenomena.  Even  this  idea  as  to 
ether  being  the  basis  of  matter  seems  to  have  lurked 
in  the  all-embracing  mind  of  Newton,  for  he  says  : 
'Thus,  perhaps,  may  all  things  be  originated  from 
aether.' l  In  later  years,  Helmholtz  accepted  Lord 
Kelvin's  idea  and  contributed  remarkable  mathematical 
papers  in  its  support.  The  element,  according  to  this 
conception,  is  neither  a  solid  atom,  nor  a  mass  of 
atoms,  but  a  whirl  in  a  fluid  ether.  The  molecules 
of  a  particular  element  have  one  invariable  and 
unchangeable  mass ;  when  the  substance  is  incan- 
descent, its  molecules  are  vibrating,  and  emit  the 
same  kind  of  light,  being  tuned,  as  it  were,  to 
definite  pitches.  As  Levering  said  :  '  The  music  of 
the  spheres  has  left  the  heavens  and  condescended  to 
.  rhythmic  molecules.  There  is  no  birth  or  death  or 
variation  of  species.  If  other  masses  than  the  precise 
ones  which  represent  the  elements  have  been  elimin- 
ated, where,  asks  Clerk  Maxwell,  have  they  gone  ? 
The  spectroscope  does  not  show  them  in  the  stars  or 
nebulae.  The  hydrogen  and  sodium  of  the  remotest 
space  is  in  unison  with  the  hydrogen  and  sodium  or 
the  earth.'2  Finally,  the  theory  of  vortex  motions 
has  made  it  possible  to  understand  in  some  measure 
the  transmission  of  magneto-electric  effects  through  an 
intervening  medium,  and  it  has  also  helped  to  dispel 

1  Letter  to  the   Secretary   of  the    Royal    Society,  Henry  Oldenburg, 
Jan.  1676.     (Hist,  of  Royal  Society,  by  T.  Birch,  vol.  iii.,  p.  250). 

-  Joseph  Levering.     Address  to  American  Association  for  Advancement 
of  Science.     Hartford,  Aug.  14,  1874. 
I99 


HERMANN  VON  HELMHOLTZ 

the  fiction  of  action  at  a  distance.  Some  idea  may 
be  formed  of  the  possible  variety  of  forms  of  vortex 
atoms  by  simply  looking  at  the  illustrations  of  Pro- 
fessor Tait's  remarkable  paper  upon  Knots.1 

1  Scientific  Papers,  vol.  i.,  p.  273. 


200 


CHAPTER    XV 

HELMHOLTZ    IN    BERLIN — PHYSICAL    RESEARCHES 
CONTINUED 

IN  1868,  Helmholtz  pressed  farther  the  analogy 
between  the  equations  of  fluid  motion  and  those 
of  electricity  and  heat  in  a  paper  on  movements  in 
discontinuous  fluids.  He  also  endeavoured  to  account 
for  certain  discrepancies  that  exist  between  theory 
and  experiment.  He  found  that  such  discrepancies 
are  greatest  in  cases  where  the  current  enters  a  wide 
space  through  an  opening  having  sharp  edges.  In 
such  circumstances,  discontinuity  of  the  fluid  occurs  ; 
it  is,  as  it  were,  torn  asunder,  and  a  surface  of  separa- 
tion is  formed  with  rounded  edges  ;  rupture  will  only 
occur  with  increased  velocity  of  the  fluid.  These 
investigations  have  also  a  practical  bearing  on  the 
theory  of  the  flow  of  water  through  cylindrical  pipes, 
and  on  the  origin  of  rotational  movements.  In  this 
memoir,  also,  he  showed  the  applications  of  several 
formulae  to  electricity,  in  which  the  co-ordinates  are 
expressed  as  functions  of  the  potential  and  its  con- 
jugate functions.  For  example,  he  discussed  the  case 

201 


HERMANN  VON  HELMHOLTZ 

of  an  electrified  plate  of  finite  size  parallel  to  an  infinite 
plane  surface  connected  with  the  earth. 

It  was  important  for  hydrodynamical  theories  to 
determine  with  exactitude  the  internal  friction  of 
fluids.  Two  important  researches  were  undertaken. 
In  one,  along  with  G.  von  Piotrowski,  Helmholtz 
observed  the  friction  that  occurs  at  the  borders  of 
the  fluid  where  it  touches  the  surrounding  medium. 
A  globe  of  metal,  having  a  polished  and  gilded 
interior,  was  filled  with  various  fluids  and  swung 
round  a  perpendicular  axis,  while  the  delay  in  the 
vibrations  or  movements  at  the  border  was  observed 
and  measured  by  means  of  a  mirror  reflecting  a  beam 
of  light  into  a  telescope.  This  method  was  similar 
to  that  previously  employed  by  Bessel,  whose  obser- 
vations and  mathematical  deductions  are  fully  dis- 
cussed. In  long  thin  tubes,  as  was  shown  by 
Poiseuille,  the  upper  layer  of  fluid  adheres  firmly  to 
the  walls  of  the  tube,  but  this  was  shown  not 
to  be  the  case  with  the  polished  globe  when  filled 
with  water,  though  it  was  true  as  regarded  alcohol 
and  ether.  The  other  research  dealing  with  ques- 
tions regarding  friction  was  mathematical,  and  com- 
pleted the  theory  of  stationary  or  static  streams  in 
fluids. 

The  theorem  as  to  the  geometrically  similar  move- 
ments of  fluid  bodies,  issued  in  1873,  made  it  possible 
to  draw  some  practical  conclusions  regarding  the 
steering  of  balloons,  with  which  the  behaviour  of  a 

202 


HELMHOLTZ  IN  BERLIN 

ship  was  compared  and  contrasted.  Helmholtz  sug- 
gested cigar-shaped  balloons.  The  conditions  of  flight 
also  arrested  his  attention.  He  was  of  opinion,  on 
theoretical  grounds,  that  the  great  condor  of  the 
Andes  has  probably  reached  that  limit  of  size  at 
which  a  bird  can  still  soar  in  the  air  by  the  action 
of  the  muscles  of  its  wings  ;  and  he  despaired  of 
man  ever  being  able  to  lift  himself  from  the  ground 
by  muscular  action  alone,  however  ingeniously  applied. 


3.  On  Electrodynamics  and  Theories  of  Electricity. 

Electrical  phenomena  of  all  kinds  irresistibly 
attracted  Helmholtz  throughout  his  whole  life,  and 
his  works  show,  from  the  tract  on  the  conservation  of 
energy  of  1847  d°wn  to  a  paper  on  Clerk  Maxwell's 
Theory  of  the  Movements  of  the  Ether,  published 
in  1893,  t^le  vear  before  his  death,  a  succession  of 
about  thirty  communications,  mostly  all  of  the  first 
importance.  So  early  as  1851  he  measured  the 
duration  of  induced  electrical  currents. 

For  many  years  the  conception  of  the  action  of 
Newton's  law  of  gravitation  dominated  the  minds  of 
physicists,  and  suggested  the  notion  of  c  action  at  a 
distance.'  That  is  to  say,  it  was  supposed  to  be  possible 
that  one  body  might  act  upon  another  without  the  exist- 
ence of  any  tangible  or  intangible  intervening  medium. 
And  yet  this  was  not  the  opinion  of  Newton  himself, 
for,  in  his  third  letter  to  Bentley,  he  wrote  : — c  That 
203 


HERMANN  VON  HELMHOLTZ 

gravity  should  be  innate,  inherent,  and  essential  to 
matter,  so  that  one  body  may  act  upon  another  at  a 
distance,  through  a  vacuum,  without  the  mediation 
of  anything  else,  by  and  through  which  their  action 
and  force  may  be  conveyed  from  one  to  another,  is  to 
me  so  great  an  absurdity,  that  I  believe  no  man,  who 
has  in  philosophical  matters  a  competent  faculty  of 
thinking,  can  ever  fall  into  it.' 

The  notion  of  action  at  a  distance  was  the  first 
conception  of  electrical  action,  and  it  found  expression 
especially  in  the  well-known  law  of  Wilhelm  Weber. 
He  endeavoured  to  explain  electrical  attractions  by 
the  assumption  of  a  force  acting  in  straight  lines,  and 
following  the  same  laws  as  the  laws  of  gravitation. 
This  was  supported  by  Coulomb.  Suppose  two 
electrified  bodies  near  each  other,  then  the  intensity 
of  the  force  is  inversely  proportional  to  the  square  of 
the  distance  between  the  two  quantities  of  electricity 
on  their  respective  surfaces  and  directly  proportional 
to  the  product  of  the  two  quantities.  There  is  also 
repulsion  between  like,  and  attraction  between  unlike, 
electrical  states.  Further,  it  was  supposed  that  this 
force  was  instantaneously  propagated  through  space. 
Weber  differed  from  Coulomb,  in  holding  that  both 
the  velocity  at  which  the  electric  quantities  approached 
or  separated,  and  also  the  acceleration  of  the  velocity, 
had  an  influence  on  the  amount  of  force  exercised 
between  the  two  bodies.  Other  similar  hypotheses 
were  in  vogue,  such  as  those  of  F.  E.  Neumann, 
204 


HELMHOLTZ  IN  BERLIN 

his  son,  C.  Neumann,  Riemann,  Grassmann,  and 
Clausius.  According  to  Helmholtz,  the  field  of 
electrodynamics  was  at  this  time  a  pathless  desert. 
('So  war  das  Gebiet  der  Elektrodynamik  um  jene 
Zeit  zu  einer  unwegsamen  Wiiste  geworden.') l 
The  theory  of  electrical  action  at  a  distance  gave 
little  satisfaction. 

Then  arose  the  conception  that  actions  between 
electrified  bodies  occupied  time  and  required  an  in- 
tervening medium.  The  turning-point  between  the 
old  and  the  new  conceptions  was  reached  in  1837, 
when  Faraday  published  his  experiments  on  the 
specific  inductive  capacity  of  substances.  Faraday 
proved  that  the  force  of  repulsion  between  two  similar 
quantities  of  electricity  depends  not  only  on  the 
quantities  and  on  their  distance  apart,  but  also  on  the 
intervening  medium.2  The  English  philosopher  had 
a  genius  for  experiment,  and  he  was  guided  by  a 
marvellous  insight  into  hidden  processes.  As  has 
been  well  said  by  Clerk  Maxwell, — '  Faraday,  in  his 
mind's  eye,  saw  lines  of  force  traversing  all  space, 
where  the  mathematicians  saw  centres  of  force 
attracting  at  a  distance ;  Faraday  saw  a  medium 
where  they  saw  nothing  but  distance  ;  Faraday  sought 
the  seat  of  the  phenomena  in  real  actions  going  on 
in  the  medium,  they  were  satisfied  that  they  had 

1  Introduction    by  Helmholtz    to    Die  Primsifien  der  Mechanik,  von 
Heinrich  Hertz,  s.  xi. 

2  An  excellent  account  of  electrical  units  is  given  by  Magnus  Maclean 
in  his  work  on  Physical  Units.     London,  1896. 

205 


HERMANN  VON  HELMHOLTZ 

found  it  in  a  power  of  action  at  a  distance  impressed 
on  the  electric  fluid.'  Lord  Kelvin  writes, — '  Faraday, 
without  mathematics,  divined  the  result  of  mathe- 
matical investigation  ;  and  what  has  proved  of  infinite 
value  to  the  mathematicians  themselves,  he  has  given 
them  an  articulate  language  in  which  to  express 
their  results.  Indeed,  the  whole  language  of  the 
magnetic  field  and  lines  of  force  are  Faraday's.  It  must 
be  said  for  the  mathematicians  that  they  greedily 
accepted  it,  and  have  ever  since  been  most  zealous  in 
using  it  to  the  best  advantage.' 

It  was  one  of  Helmholtz's  mental  qualities,  that 
he  was  never  satisfied  with  an  inadequate  explanation. 
He  examined  all  the  theories  of  electrical  action 
and  found  them  insufficient.  His  studies  were  at 
first  of  a  critical  nature,  without  experimental  investi- 
gation. He  showed  that  certain  consequences  of 
Weber's  law  were  inconsistent  with,  or  even  contra- 
dicted, the  law  of  the  conservation  of  energy,  although, 
on  the  other  hand,  they  gave  a  satisfactory  explana- 
tion of  many  of  the  facts.  Helmholtz  demonstrated 
that  the  law  led  to  the  idea  of  infinite  speed,  and 
also  implied  that  the  centre  of  gravity  of  static 
electricity  was  changeable.  With  Coulomb's  state- 
ment, that  electric  forces  act  through  space  similar  to 
gravitation,  and  follow  substantially  the  same  law,  he 
was  more  in  accord.  He  accepted  Neumann's  notion 
or  law  of  potential  with  reservations. 

The  special  work  of  Helmholtz  on  electrodynamics 
206 


HELMHOLTZ  IN  BERLIN 

has  been  thus  shortly  stated  by  Professor  Riicker  : l 
'  From  1870  onwards,  Helmholtz  published  an  im- 
portant series  of  papers  on  the  theory  of  electro- 
dynamics. His  point  of  departure  was  the  discussion 
of  the  mutual  action  of  two  current  elements.  An 
expression  for  the  potential  of  two  such  elements  had 
been  formulated  by  F.  E.  Neumann,  which  differed 
from  those  deduced  from  the  theories  of  W.  \Veber 
and  Clerk  Maxwell  respectively.  All  three  gave 
identical  results  in  the  case  of  closed  circuits.  Tak- 
ing the  elder  Neumann's  formula  as  the  groundwork 
of  his  investigations,  Helmholtz  sought  to  find  the 
terms  which  must  be  added  to  it,  so  as  to  produce 
the  most  general  expression  consistent  with  the 
known  behaviour  of  closed  circuits.  The  result  was 
an  expression  consisting  of  the  sum  of  two  terms, 
which  were  multiplied  respectively  by  i  +  k  and 
i  -  ^,  where  k  is  an  undetermined  constant.  The 
expression  is  equivalent  to  that  given  by  Weber 
when  k  =  -  i,  to  that  given  by  F.  E.  Neumann 
when  k  =  i,  and  is  in  accord  with  Maxwell's  theory 
when  k  =  o.  It  was  then  proved  that  if  k  is 
negative  the  equilibrium  of  electricity  at  best  must 
be  unstable,  so  that  motion,  when  once  established, 
would  increase  of  its  own  accord,  and  lead  to  infinite 
velocities  and  densities.  The  assumption  was,  in  fact, 
a  violation  of  the  law  of  the  conservation  of  energy 

1  Riicker,  Obituary  Notice  of  Helmholtz,  Proc.  Roy.  Sac.,  vol.  lix.,  No. 
355,  P-  27- 

207 


HERMANN  VON  HELMHOLTZ 

in  the  sense  that  two  electrified  particles  starting 
with  a  finite  velocity  would,  within  a  finite  dis- 
tance, acquire  infinite  speed,  and  therefore  infinite 
energy.  ...  It  remains,  however,  to  discuss  the 
case  where  k  was  equal  to  or  greater  than  zero. 
The  most  interesting  part  of  this  investigation  was 
the  application  of  the  generalised  formula  to  the 
propagation  of  electrical  and  magnetic  disturbances 
through  bodies  capable  of  electrical  or  magnetic 
polarisation.  These  properties  were  treated  inde- 
pendently. .  .  .  Both  longitudinal  and  transversal 
electric  disturbances  can  be  propagated  in  unmagnet- 
isable  dielectrics.  The  velocity  of  the  transversal 
undulations  in  air  depends  on  the  absolute  suscepti- 
bility of  the  medium.  If  this  is  very  large  the 
velocity  is  the  same  as  that  of  light.  The  velocity 
of  the  longitudinal  waves  is  equal  to  that  of  the 
transversal  waves  multiplied  by  the  factor  i/^,  and 
by  a  constant  which  depends  on  the  magnetic  con- 
stitution of  the  air.  In  conductors  the  waves  are 
rapidly  damped.  If  the  insulator  is  magnetisable,  the 
magnetic  longitudinal  oscillations  have  an  infinite 
velocity,  the  transversal  magnetic  oscillations  are  per- 
pendicular to  the  transversal  electrical  oscillations, 
and  are  propagated  with  the  same  velocity.  In  the 
particular  cases  when  k  =  o  the  longitudinal  waves 
of  electricity  have  also  an  infinite  velocity,  and  the 
theory  is  then  in  close  accord  with  that  of  Maxwell, 
provided  that  the  absolute  specific  inductive  capacity 
208 


HELMHOLTZ  IN  BERLIN 

of  the  air  is  great  enough  to  make  the  common 
velocity  of  the  electrical  and  magnetic  transversal 
undulations  equal  to  that  of  light.' 

Finding  the  notion  of  action  at  a  distance  in- 
consistent with  dynamic  principles  and  with  ex- 
periment, he  abandoned  it  and  accepted  Faraday's 
principle.  Then  followed,  as  the  years  went  by, 
papers  on  the  origin  of  electric  currents  and  on 
their  action  in  circuit,  on  galvanic  polarisation 
of  fluids  free  from  gas,  on  the  electrolysis  of 
water,  on  galvanic  currents  due  to  differences  of 
concentration  of  fluids,  on  electric  border-plates,  on 
currents  on  polarised  platinum,  on  the  galvanic 
polarisation  of  mercury,  and  on  the  capillary  electro- 
meter. In  some  of  these  papers  the  method  followed 
is  less  mathematical  and  more  that  of  experiment 
and  induction  ;  but  in  all  the  fundamental  principle 
is  the  conservation  of  energy.  In  the  tract  on  the 
conservation  of  energy  he  had  shown  long  before  that 
if  the  phenomena  of  Oersted  and  Ampere  be  assumed, 
that  is,  if  a  wire  carrying  an  electric  current  is 
impelled  across  the  lines  of  magnetic  force,  then  the 
phenomenon  discovered  by  Faraday  follows  necessarily, 
namely,  a  conductor  moved  across  the  lines  of 
magnetic  force  shows  an  electromotive  force  whose 
intensity  can  be  determined  by  the  application  of 
the  equation  of  energy.1 

Ampere    had   stated    the   laws    of  action    between 

'  Tait,  op.  cit.,  p.  89. 
O 


HERMANN  VON  HELMHOLTZ 

conductors  carrying  currents,  and  he  showed  that 
the  action  of  a  small  closed  current  at  a  distance  is 
the  same  as  that  of  a  small  magnet  placed  in  the 
centre  of  the  closed  circuit,  provided  that  the  axis 
of  the  magnet  is  at  right  angles  to  the  plane  of 
the  closed  circuit,  and  that  its  magnetic  moment  is 
equal  to  the  product  of  the  area  of  the  closed 
circuit  into  the  current.  This  subject  was  extended 
mathematically  by  Helmholtz. 

Helmholtz  introduced  a  new  method  of  research 
into  electrical  questions  by  bringing  in  the  idea  of 
convection  in  the  distribution  of  electricity,  that  is, 
the  conveyance  of  electricity  from  one  point  to  another 
by  the  movement  of  the  material  elements  carrying  it. 
It  was  important  to  determine  whether  or  not  the 
magnetic  effects  of  an  electric  current  were  identical 
with  those  produced  by  the  displacement  of  matter 
carrying  an  electrostatic  charge.  The  experimental 
research  on  this  subject  was  carried  out  in  Helmholtz's 
laboratory  by  the  well-known  American  physicist, 
H.  A.  Rowland,  and  the  results  were  published  in 
1876.  Electrical  convection  currents  throw  some 
light  on  the  movement  of  electricity  in  unclosed 
conductors  ;  while  in  electrolysis  the  gases  dissolved 
in  the  fluid  may  also  carry  charges  of  electricity  by 
convection.  It  was  proved  that  a  revolving  charged 
conductor  behaves  like  a  ring-shaped  electric  current. 

With    another    American    electrician,    E.    Root, 
Helmholtz,  also  in    1876,  examined  the  polarisation 


HELMHOLTZ  IN  BERLIN 

effects  of  the  occlusion  of  hydrogen  on  thin  plates 
of  palladium  and  platinum.  They  found  that  if  a 
stream  of  hydrogen  is  directed  to  one  side  of  a 
thin  platinum  plate  by  electrolysis,  its  presence  is 
soon  felt  on  the  other  side  of  the  plate  by  the  plate 
becoming  more  positive,  and  they  showed  that  what 
was  required  by  theory  was  fulfilled  by  experiment. 

In  these  investigations  Helmholtz  made  many 
subsidiary  discoveries.  Lord  Kelvin  and  he  inde- 
pendently established  the  reciprocal  property  of  the 
electric  charge  of  one  conductor  on  another.  Thus 
the  potential  of  a  body  A  due  to  a  unit  charge 
on  B  is  equal  to  the  potential  of  B  due  to  a  unit 
charge  on  A.  He  also  invented  a  double  galvano- 
meter, which  was  a  modification  of  that  of  Gaugain. 
In  the  instrument  of  the  latter  the  magnet  was 
suspended,  not  at  the  centre  of  the  coil,  but  at  a 
point  on  the  axis  at  a  distance  from  the  centre  equal 
to  half  the  radius  of  the  coil.  Helmholtz  greatly 
improved  the  instrument,  and  made  it  more  trust- 
worthy by  placing  a  second  coil,  equal  to  the  first, 
at  an  equal  distance  on  the  other  side  of  the  magnet.1 
He  also  constructed  an  electro-dynamic  balance  not 
affected  by  the  magnetism  of  the  earth. 

On  April  5,  1881,  Helmholtz  delivered  the 
Faraday  lecture  to  the  Chemical  Society  On  the 
Modern  Development  of  Faraday's  Conception  of  Elec- 
tricity, in  which  he  gave  an  interesting  estimate  of 

1  Jamin  et  Bouty,  Cours  de  Physique,  t.  iv.  2,  p.  133.     Paris,  1883. 
211 


HERMANN  VON  HELMHOLTZ 

the  great  English  physicist.1  His  words  in  opening 
the  lecture  are  so  characteristic  of  Helmholtz  him- 
self as  to  merit  quotation :  '  The  facts  which  he 
[Faraday]  discovered  are  universally  known.  Every 
physicist,  at  present,  is  acquainted  with  the  rotation 
of  the  plane  of  polarisation  of  light  by  magnetism, 
with  dielectric  tension  and  diamagnetism,  and  with 
the  measurement  of  the  intensity  of  galvanic  currents 
by  the  voltameter,  while  induced  currents  act  on 
the  telephone,  are  applied  to  paralysed  muscles,  and 
nourish  the  electric  light.  Nevertheless,  the  funda- 
mental conceptions  by  which  Faraday  was  led  to 
these  much  admired  discoveries  have  not  received 
an  equal  amount  of  consideration.  They  were  very 
divergent  from  the  trodden  path  of  scientific  theory, 
and  appeared  rather  startling  to  his  contemporaries. 
His  principal  aim  was  to  express  in  his  new  con- 
ceptions only  facts,  with  the  least  possible  use  of 
hypothetical  substances  and  forces.  This  was  really 
an  advance  on  general  scentific  method,  destined  to 
purify  science  from  the  last  remnants  of  metaphysics. 
Faraday  was  not  the  first,  and  not  the  only  man, 
who  has  worked  in  this  direction,  but  perhaps  no- 
body else  at  his  time  did  it  so  radically.  But  every 
reform  of  fundamental  and  leading  principles  intro- 
duces new  kinds  of  abstract  notions,  the  sense  of 
which  the  reader  does  not  catch  in  the  first  instance. 
Under  such  circumstances,  it  is  often  less  difficult 

1   Trans .  of  the  Chemical  Society,  p.  277. 
212 


HELMHOLTZ  IN  BERLIN 

for  a  man  of  original  thought  to  discover  new  truth 
than  to  discover  why  other  people  do  not  understand 
and  do  not  follow  him.  This  difficulty  must  increase 
in  Faraday's  case,  because  he  had  not  gone  through 
the  same  common  course  of  scientific  education  as 
the  majority  of  his  readers.  Now  that  the  mathe- 
matical interpretation  of  Faraday's  conceptions  re- 
garding the  nature  of  electric  and  magnetic  forces  has 
been  given  by  Clerk  Maxwell,  we  see  how  great  a 
degree  of  exactness  and  precision  was  really  hidden 
behind  the  words,  which,  to  Faraday's  contemporaries, 
appeared  either  vague  or  obscure  ;  and  it  is  in  the 
highest  degree  astonishing  to  see  what  a  large  number 
of  general  theorems,  the  methodical  deduction  of 
which  requires  the  highest  powers  of  mathematical 
analysis,  he  found  by  a  kind  of  intuition,  with  the 
security  of  instinct,  without  the  help  of  a  single 
mathematical  formula.  I  have  no  intention  of  blam- 
ing his  contemporaries,  for  I  confess  that  many  times 
I  have  myself  sat  hopelessly  looking  upon  some 
paragraph  of  Faraday's  description  of  lines  of  Force, 
or  of  the  galvanic  current  being  an  axis  of  power, 
etc.  A  single  remarkable  discovery  may,  of  course, 
be  the  result  of  a  happy  accident,  and  may  not 
indicate  the  possession  of  any  special  gift  on  the 
part  of  the  discoverer  ;  but  it  is  against  all  rules  of 
probability,  that  the  train  of  thought  which  has  led 
to  such  a  series  of  surprising  and  unexpected  dis- 
coveries, as  were  those  of  Faraday,  should  be  with- 
213 


HERMANN  VON  HELMHOLTZ 

out  a  firm,  although  perhaps  hidden,  basis  of  truth. 
We  must  also  in  his  case  acquiesce  in  the  fact,  that  the 
greatest  benefactors  of  mankind  usually  do  not  obtain 
a  full  reward  during  their  lifetime,  and  that  new  ideas 
need  the  more  time  for  gaining  general  assent  the 
more  really  original  they  are,  and  the  more  power  they 
have  to  change  the  broad  path  of  human  knowledge.' 

The  lecture,  however,  was  not  merely  a  panegyric 
of  Faraday.  Helmholtz  unfolded  to  the  English 
chemists  the  theory  of  electrolysis,  in  its  most 
modern  form,  as  moulded  by  the  law  of  the  con- 
servation of  energy,  and  the  laws  of  electrolysis 
discovered  by  Faraday  himself.  Electricity  can  pass 
from  the  fluid  to  the  electrodes  only  under  condi- 
tions of  equivalent  chemical  decomposition,  which  is 
brought  about  by  the  electrical  forces  splitting  up 
the  chemical  compounds  present.  Helmholtz  proved 
by  calculation  that  the  electric  forces  are  quite 
sufficient  for  this  work,  as  shown  by  the  unexpected 
magnitude  of  the  electrical  equivalents  that  change 
places  during  the  process. 

As  already  stated,  p.  206,  Helmholtz  found  that  all 
the  hypotheses  of  electrical  action,  such  as  those  of 
Weber,  the  Neumanns,  Riemann  and  others,  ex- 
plained certain  of  the  facts.  For  example,  he  found 
that  they  all  accounted  for  the  phenomena  of  elec- 
trical currents  in  closed  circuits,  but  they  did  not 
do  so  for  conductors  which  end  in  insulating  non- 
conductors, or  what  might  be  called  open  or 
214 


HELMHOLTZ  IN  BERLIN 

unclosed  conductors.  He  was  also  of  opinion  that 
Wilhelm  Weber's  supposition  that  electrical  quantities 
had  inertia,  like  ponderable  bodies,  was  highly  improb- 
able. In  1879,  Helmholtz  set  as  a  prize  research 
for  his  students  this  question  of  the  inertia  of 
electricity,  and,  in  1880,  it  was  won  by  Heinrich 
Hertz,  who  showed  that  if  it  has  inertia  at  all,  the 
latter  could  only  have  an  influence  of  the  smallest 
degree  conceivable.  This  was  the  beginning  of  the 
famous  work  of  Hertz,  which  resulted  in  the  ex- 
perimental demonstration  of  Maxwell's  magneto- 
electric  waves,  and  has  led  to  the  invention  of 
wireless  telegraphy. 

The  subject  of  electrical  oscillations  was  investi- 
gated by  Helmholtz  in  1869  and  1871.  In  1869 
he  caused  his  pendulum  myograph  to  close  two 
circuits  at  short  but  measurable  intervals  of  time. 
Oscillations  were  thus  produced  in  a  secondary 
circuit,  the  terminals  of  which  were  led  off  to  a 
Leyden  jar.  The  secondary  circuit  was  then  broken, 
and  the  electrical  oscillation  was  transmitted  to  the 
sciatic  nerve  of  a  frog-muscle  preparation.  The 
number  of  twitches  could  thus  be  recorded.  As  the 
time  between  the  completing  of  the  primary  and  the 
breaking  of  the  secondary  current  was  increased  in 
successive  experiments,  alternations  in  the  violence 
of  the  twitchings  of  the  muscle  were  noticed,  and 
in  all  forty-five  minima  were  observed.1  In  1871, 

1  Riicker,  op.  cit.,  p.  27. 
215 


HERMANN  VON  HELMHOLTZ 

Helmholtz,  by  his  pendulum  methods,  determined 
the  velocity  of  the  propagation  of  electro-magnetic 
induction  at  314,400  metres  per  second. 

Faraday  had  shown  that  the  passage  of  electrical 
action  involved  time  ;  but,  what  was  of  even  greater 
importance,  he  also  demonstrated  that  electrical 
phenomena  are  brought  about  by  changes  in  in- 
tervening non-conductors,  or  dielectric  substances. 
The  seat  of  electrical  action  was  to  be  sought  in  the 
tensions  and  strains  that  occur  in  the  dielectric 
medium.  Upon  this  basis  Clerk  Maxwell  founded  his 
theory  of  electrodynamics.  This  theory,  carried  out 
to  its  logical  conclusion,  required  that  any  electric 
disturbance  should  be  propagated  through  what  had 
been  till  then  called  the  '  luminiferous '  ether. 
Suppose  a  current  passing  in  a  metallic  conductor  in 
which  there  is  a  minute  break  or  gap  filled  up  by  a 
non-conductor,  such  as  air,  the  current,  if  sufficiently 
strong,  will  pass  across  the  gap  as  a  spark.  If 
this  action  cause  a  disturbance  in  the  dielectric, 
this  disturbance  should  be  propagated  into  space  by 
the  ether  ?  An  imperfect  analogy  may  help  the 
mind  at  this  point.  What  occurs  at  the  gap 
may  be  like  the  effect  of  a  stone  dropped  into  still 
water,  when  a  wave  will  be  started  and  propagated 
from  the  centre  of  disturbance.  Another  disturbance 
will  cause  another  wave,  another  a  third  wave,  and 
so  on.  The  shorter  the  interval  of  time  between 
successive  disturbances  the  shorter  will  be  the  waves. 
216 


HELMHOLTZ  IN  BERLIN 

Is  there  anything  analogous  in  magneto-electric 
action  ?  Fitzgerald  was  the  first  to  suggest  an 
attempt  to  measure  the  length  of  electric  waves ; 
and  Helmholtz  propounded  the  question  for  a  prize 
essay  to  be  awarded  by  the  Berlin  Academy. 

It  was  reserved  for  Hertz,  the  favourite  pupil  of 
Helmholtz,  to  prove  the  correctness  of  Clerk 
Maxwell's  theory,  and  actually  to  demonstrate  the 
existence  of  electro-magnetic  waves,  or,  as  they  are 
usually  called,  the  Hertzian  Waves.  How  he 
was  led  step  by  step  to  this  great  discovery,  over- 
coming difficulties  as  they  arose,  and  going  into  this 
unknown  land  in  the  firm  belief  that  scientific  theory 
would  not  lead  him  astray,  has  been  fully  described 
by  Hertz  himself.1  He  showed  that  waves  of  electric 
energy  consist  of  displacements  transverse  to  the  direc- 
tion of  transmission,  and  are  governed  by  the  same 
laws  of  reflection,  refraction,  and  polarisation  as  those 
of  light.  Their  velocity  of  transmission  is  the  same  as 
that  of  light,  300,000  kilometres  per  second  (186,380 
miles  per  second,  in  vacuo  ;  Michelson,  1879).  As 
the  electric  oscillations  produced  by  the  Hertzian 
method  are  comparatively  few  in  number  per  second, 
when  the  velocity  of  light  is  divided  by  this  number, 
the  resultant  wave-length  is  still  found  to  be  im- 

1  Hertz.  Electric  ffa-ves.  Trans,  by  Jones,  with  preface  by  Lord 
Kelvin.  London,  1893.  See  especially  the  Introduction,  p.  I.  See  also 
a  lecture  by  Hertz  On  the  Relations  bet-ween  Light  and  Electricity,  delivered 
on  Sept.  20,  1889,  and  printed  in  his  Miscellaneous  Papers,  trans,  by 
Jones,  p.  313.  London,  1896. 

2I7 


HERMANN  VON  HELMHOLTZ 

mensely  greater  than  that  of  light,  varying  from 
decimetres  to  kilometres,  while  the  waves  that  fall  on 
the  retina,  and  constitute  what  we  call  light,  have  a 
wave-length  of  only  from  0*3  to  0-7  thousandths  of  a 
millimetre.1  Then,  by  the  principle  of  '  resonance,' 
(using  this  word  in  a  special  sense),  the  waves  may 
be  detected  as  minute  sparks,  or  by  acting  on  an 
arrangement  called  a  coherer.2  Hence  wireless  tele- 
graphy ! 

Hertz  always  referred  the  inspiration  to  Helmholtz, 
and  W.  von  Bezold  gives  his  impression  of  the 
memorable  occasion  when  Helmholtz  reported  to  the 
Academy  on  the  researches  of  his  distinguished  pupil. 
'The  impression  will  never  be  forgotten  by  any- 
one. .  .  .  The  most  intense  and  purest  joy  shone  in 
the  countenance  of  the  great  master,  who  explained  in 
eloquent  words,  and  with  the  freshness  of  youth,  the 
importance  and  influence  of  this  fundamental  work.' 
This  was  in  1888.  Six  years  later,  on  the  ist  of 
January  1894,  Hertz  died  before  the  completion  of 
his  thirty-seventh  year.  Helmholtz  wrote  of  him 
these  words  : — c  The  news  of  the  death  of  this 
favourite  of  genius  was  a  severe  shock  to  all  who 

1  Relation  between  British  and  metric  units  of  length  and  mass  : — 
i   yard  =  o'9i439i79  metre;    i  metres  1*09362311   yards  =  39*370432 
inches;    i   poundzzo'453593   kilogramme;    i   kilogrammes 2*2046212 
pounds;    also,    i    kilometre  =  1000    metres;     i     millimetre — ToVrjth 
metre  =  5*jth  inch. 

2  Kerr.     Wireless  Telegraphy.     London,  1898.     Also,  Andrew  Gray's 
Treatise  on   Electricity  and  Magnetism,  vol.  i..  London,  1898,  chap,  xi., 
for  a  full  description  of  the  Hertzian  Vibrator  and  Receiver. 

218 


HELMHOLTZ  IN  BERLIN 

recognise  the  development  of  the  individual,  both  as 
regards  mental  capacity  and  the  victory  of  the  soul 
over  the  passions  and  opposing  powers  of  nature. 
Endowed  with  the  rarest  gifts  of  mind  and  character, 
he  has  in  his  short  life  reaped  a  harvest  in  a  field  in 
which  many  of  the  most  talented  of  his  scientific 
brethren  had  laboured  in  vain.  In  classical  times  his 
death  would  have  been  regarded  as  a  sacrifice  to  the 
envy  of  the  gods.  Nature  and  fate  co-operated  in  his 
development.  In  him  we  found  all  the  qualities 
required  for  the  solution  of  the  hardest  problems  in 
science.  .  .  .  Heinrich  Hertz  appeared  to  be  pre- 
destined to  disclose  new  vistas  into  the  unpenetrated 
depths  of  nature  ;  but  all  these  hopes  were  crushed  by 
the  insidious  disease  which  slowly  and  unceasingly 
crept  on  until  it  destroyed  the  life  we  esteemed  so 
valuable.  I  myself  deeply  felt  the  loss,  as  I  have 
always  looked  on  Hertz  as  the  one  of  all  my  students 
who  had  entered  into  the  innermost  circle  of  my 
scientific  thoughts,  and  the  one  in  whose  ultimate 
development  and  success  I  dared  to  place  my  surest 
hopes.'  In  a  few  months  the  great  master  followed 
his  pupil  to  the  grave. 

Among  the  last  papers  written  by  Helmholtz  was 
one  on  Clerk  Maxwell's  theory  of  the  movements  in 
the  free  ether,  in  which  he  discussed  profound  ques- 
tions as  to  whether  it  were  free  to  move,  to  what 
extent  and  how  it  was  associated  with  gross  matter, 
and  he  shows  that  its  incompressibility  being  assumed, 
219 


HERMANN  VON  HELMHOLTZ 

all  its  changes  and  movements  can  be  deduced  from 
the  laws  of  electrodynamics,  and  the  principle  of 
least  action. 


4.    On  Meteorological  Physics. 

Like  all  brain  workers,  Helmholtz  found  it 
necessary  to  spend  part  of  the  year,  mostly  during 
the  interval  between  the  summer  and  winter  sessions 
of  academic  work,  in  the  country,  and  he  was  in  the 
habit  of  going  to  the  Alps,  to  the  south  of  France, 
and  occasionally  to  England.  One  can  readily  under- 
stand that  a  mind  like  his  was  always  receptive,  and 
that  the  sights  and  sounds  of  nature  in  the  magni- 
ficent aspect  of  mountain  and  valley,  in  the  green 
woodland  and  on  the  rocky  coast  by  the  sea,  were  a 
source  of  the  purest  enjoyment.  But  the  intellect 
never  slumbered.  Accordingly,  we  find  that  he 
endeavoured,  now  and  again,  to  explain  natural 
phenomena,  such  as  the  formation  of  clouds,  the 
mechanical  conditions  of  the  whirlpool  or  whirlwind, 
and  the  formation  of  glaciers.  It  would  be  wrong  to 
suppose  that  this  habit  of  the  scientific  analysis  of 
one's  impressions  of  natural  effects  diminishes  the 
aesthetic  enjoyment  ;  we  should  rather  conclude  that 
aesthetic  enjoyment  may  be  of  different  kinds.  The 
poet  simply  opens  his  mind  to  nature,  receiving  all 
her  impressions,  he  has  his  imagination  fired,  and  his 
heart  touched  by  the  feelings  of  beauty,  while  he 
220 


HELMHOLTZ  IN  BERLIN 

yearns  to  give  expression  to  his  feelings  in  adequate 
form.  To  him,  possibly,  an  analysis  of  how  these 
effects  are  produced  might  destroy  the  charm,  and 
might  even  lead  him  to  give  a  wrong  interpretation 
of  what  was  before  his  eyes,  as  was  the  case  when 
Goethe  attempted  to  explain  colour  by  an  utterly 
erroneous  conception.  But  the  man  of  science,  who 
has  in  him  a  love  of  nature,  and  an  imagination  akin 
to  that  of  the  poet,  and  often  more  penetrating,  must 
strive  towards  the  intellectual  satisfaction  of  under- 
standing the  methods  by  which  nature  works. 

In  one  of  his  papers  on  hydrodynamics,  Helmholtz 
refers  shortly  to  the  theory  of  tidal  action.  The 
tendency  of  tidal  movements  on  the  surface  of  a  planet 
is  to  retard  its  rotation  till  at  last  it  turns  always  the 
same  face  to  the  body  that  causes  the  tidal  motion. 
Helmholtz  was  the  first  to  point  out  that  the  reason 
why  satellites  generally  turn  the  same  face  to  their 
primary,  is  to  be  found  in  the  tides  produced  by  the 
primary  on  the  satellite  while  it  was  yet  in  the  molten 
state.1 

The  movements  of  glaciers  and  the  formation  of 
ice  arrested  his  attention,  and  it  so  happened  that  at 
that  time  the  observations  of  Rendu,  Forbes  and 
Tyndall  were  being  discussed.  Helmholtz's  contribu- 
tions to  the  ice  theory  were  published  in  1865  and  1866, 
while  he  was  in  Heidelberg.  Faraday  had  made  the 
familiar  observation  that  two  pieces  of  ice  pressed  against 

1  Tait,  Thermo-DynamicSy  p.  104. 
221 


HERMANN  VON  HELMHOLTZ 

each  other  at  zero  (centigrade)  freeze  into  one  block. 
James  Thomson,  the  brother  of  Lord  Kelvin,  had 
explained  this  by  showing  that  pressure  causes  a 
lowering  of  the  freezing  point.  James  Thomson  de- 
duced this  fact  from  the  mechanical  theory  of  heat. 
Lord  Kelvin  soon  after  gave  the  complete  theory 
connecting  melting  point  and  pressure,  and  verified 
by  experiment  his  brother's  calculation  that  each  in- 
crease of  a  pressure  of  one  atmosphere  causes  a 
lowering  of  the  freezing  point  to  Ty^  of  a  degree 
cent.  A  mixture  of  snow  and  ice  becomes  colder 
as  pressure  increases,  just  as  theory  requires.  In 
Faraday's  experiment  mentioned  above,  some  free 
heat  becomes  latent  during  pressure,  a  part  of  the  ice 
along  the  side  of  the  block  melts  and  then  freezes 
again,  cementing  the  blocks  into  one  piece.  These 
facts,  and  also  the  remarkable  phenomenon  of  the 
well-known  movements  of  a  hard,  and,  in  popular 
belief,  a  brittle  body,  like  ice  in  great  glaciers, 
were  originally  accounted  for  by  regarding  ice  as  a 
viscous  fluid,  a  suggestion  due  to  Rendu,  a  Savoyard 
priest,  and  very  fully  developed  by  the  celebrated 
natural  philosopher,  James  Forbes.  Helmholtz,  by 
a  large  number  of  experiments,  in  which  ice  was 
submitted  to  varying  degrees  of  pressure,  succeeded 
in  imitating  the  formation  of  glacial  ice.  Lord 
Kelvin  also  showed  that  cobbler's  wax  behaved  like 
a  viscous  fluid.  In  the  course  of  months  or  years, 
it  will  gradually  flow  down  an  inclined  plane  as  a 

222 


HELMHOLTZ  IN  BERLIN 

glacier  flows  down  a  valley,  showing  the  curves  and 
stream  lines  as  in  the  true  glacier.  It  is  a  curious 
sight  to  watch  corks,  if  left  to  themselves  for  a 
long  time  on  the  surface  of  the  wax,  ultimately 
float  on  it,  just  as  bodies  left  on  the  surface  of  a 
glacier  may  by-and-by  be  found  deeply  embedded  in 
the  apparently  brittle  substance. 

In  one  of  his  lectures  Helmholtz  gives  an  explana- 
tion of  waterspouts.  He  shows  that  the  whirling 
water  forms  a  vertical  tube  full  of  air.  Probably  his 
most  interesting  contribution  to  meteorological  physics 
is  contained  in  two  papers  on  the  movements  of  the 
air  published  in  1888  and  1889.  This  was  followed 
by  one  in  1890  on  the  Energy  of  Winds  and  Waves.1 
In  these  he  develops  the  mathematical  theory  of  the 
formation  of  cloud  strata.  It  is  said  that  in  one  of 
his  Alpine  excursions  he  saw,  from  the  summit  of  the 
Rigi,  the  grand  spectacle  of  a  table-land  of  clouds 
below  him,  and  the  appearance  suggested  that  of 
waves  on  the  sea  seen  from  the  height  of  a  rocky 
coast.  The  formation  of  cloud  waves  was  suggested 
from  the  formation  of  water  waves,  the  fundamental 
idea  being  that  a  plane  surface  of  water  over  which  a 
wind  of  uniform  velocity  is  blowing  is  in  a  state  of 
unstable  equilibrium,  and  that  waves  thus  originate. 
Here  we  have  two  fluids,  air  and  water,  of  different 
densities,  gliding  over  each  other.  While  friction  in  the 
upper  regions  of  the  air  must  be  very  slight,  it  will 

1  Whsenschaftl.  Abhandlungen,  Bd.  iii.,  s.  289  5  8.  309  ;  s.  333. 
223 


HERMANN  VON  HELMHOLTZ 

be  found  at  surfaces  of  separation  between  two  layers 
and  along  the  borders  of  rotating  masses. 

Helmholtz  drew  special  attention  to  the  manner 
in  which,  according  to  the  kinetic  theory  of  gases, 
viscosity  and  interchange  of  temperature  take  place 
across  such  surfaces  of  separation.  We  may  suppose 
that  in  the  upper  regions  of  the  atmosphere  there 
are  contiguous  layers  of  air  of  different  densities, 
temperatures  and  velocities.  If  no  watery  vapour 
condenses  at  the  surfaces  across  which  interming- 
ling takes  place  nothing  will  be  seen.  But  should 
there  be  condensation  of  vapour,  clouds  will  be 
formed ;  and  then,  just  as  wind  raises  waves  on 
the  surface  of  the  ocean,  so  cloud  waves  will  be 
formed  on  the  side  of  the  less  dense  layer.  The 
action  will  not  take  place  in  a  quiet  steady  manner, 
but  by  fits  and  starts,  being,  indeed,  a  case  of  dis- 
turbed equilibrium.  The  effect  is  well  seen  in  the 
beautiful  wavy  appearance  of  barred  cirrhi  clouds,  in 
which  the  shining  white  bars  correspond  to  the  wave- 
troughs,  and  the  thin  translucent  bars,  through  which 
the  light  of  the  blue  sky  penetrates,  to  the  wave  crests. 
Helmholtz,  at  Cap  d'Antibes,  measured  the  velocity 
of  the  wind  with  an  anemometer,  and  counted  the 
number  of  waves  on  a  given  surface  of  sea,  and  thus 
obtained  data  on  which  to  base  his  calculations.  He 
thus  found  the  connection  between  the  strength  of  the 
wind  and  the  length  of  the  waves.  The  water  waves 
were  compared  as  to  length  with  cloud  waves.  A 
224 


HELMHOLTZ  IN  BERLIN 

moderate  wind  blowing  over  the  surface  of  water 
will  give  rise  to  waves  of  about  a  metre  in  length  (a 
little  more  than  a  yard)  ;  the  same  waves,  in  cloudland, 
at  the  border  of  two  layers  of  air,  differing  in  tempera- 
ture by  10°  C.  will  have  a  length  of  two  to  five  kilo- 
metres (about  2^-  miles).  Sea  waves  may  reach  a 
length  of  five  to  ten  metres  (say  12  yards),  and 
as  these  would  correspond  to  cloud  waves  of  from 
fifteen  to  twenty  kilometres  (say  over  10  miles),  we 
can  grasp  the  notion  that  one  of  these  long  cloud 
waves  may,  at  a  particular  time,  cover  all  the  sky 
above  our  head.  That  these  views  of  Helmholtz  on 
cloud  formation  are  correct,  has  been  supported  by 
many  observations  since  made  in  balloon  voyages. 
It  has  always  been  found  that  in  traversing  regions 
in  which  there  are  great  plains  of  cirrhi  clouds,  a 
sudden  change  of  temperature  is  noticed  in  passing 
from  one  layer  of  air  into  the  other. 

5.   On  Physical  Optics. 

A  slight  sketch  has  already  been  given  in  Chapter 
VIII.  of  Helmholtz's  researches  in  physiological  optics, 
and  the  whole  is  narrated  in  full  detail  in  a  new  edition 
of  his  great  work,  Handbuch  der  physiologischen  Optik^ 
published  in  1894,  the  year  of  his  death.  In  this 
work  the  dioptrics  of  the  eye  are  fully  discussed,  with 
a  wealth  of  illustration  and  mathematical  power  that 
is  truly  astonishing.  The  laws  of  refraction  from 
p 


HERMANN  VON  HELMHOLTZ 

spherical  surfaces,  the  properties  of  cardinal  points, 
and  the  theorems  of  Gauss  relative  to  the  refractive 
powers  of  centred  systems  of  spherical  surfaces, — all 
matters  relating  to  what  may  well  be  called  physical 
optics, — are  discussed,  so  that,  in  forming  an  estimate 
of  all  that  Helmholtz  has  accomplished  in  this  depart- 
ment of  science,  the  treatment  of  these  subjects  in  a 
work  mainly  physiological  must  not  be  forgotten. 
Nine  papers,  however,  are  enumerated  in  his  collected 
works  as  specially  belonging  to  physical  optics.  Five 
of  these  relate  to  colour,  and  might  well  have  been 
included  in  the  list  of  fifteen  works  on  physiological 
optics,  so  that  only  four  remain.  One  of  these, 
published  in  1867,  is  a  mathematical  essay  dealing 
mainly  with  the  action  of  lenses;  two,  issued  in  1873 
and  1874,  deal  with  the  higher  optical  principles  of 
the  compound  microscope  and  the  limits  of  magnifica- 
tion ;  and  the  last,  which  was  also  issued  in  1874, 
relates  to  the  theory  of  anomalous  dispersion.  Finally, 
in  1892,  there  appeared  a  paper,  important  from  a 
theoretical  point  of  view,  in  which  he  applied  Clerk 
Maxwell's  electro-magnetic  theory  of  light  to  explain 
the  dispersion  of  colour.1 

In  this  connection,  and  as  it  is  a  matter  of  practical 
interest,  it  may  be  pointed  out  that  Helmholtz  was 
often  in  the  habit  of  magnifying  small  movements 
by  reflecting  a  beam  of  light  from  a  small  mirror 

1  All  the  papers  on  light  appear  in  Bd.  ii.  Wisienschaftl.  Abhandlungen  ; 
that  on  colour  dispersion  in  Bd.  iii.,  s.  505. 
226 


HELMHOLTZ  IN  BERLIN 

attached  to  a  suitable  part  of  the  apparatus  that 
was  in  motion.  But  he  was  not  the  inventor  of 
this  method,  as  has  sometimes  been  erroneously 
stated.  PoggendorfF,  in  Vol.  VII.  of  his  Annalen^ 
issued  in  1826,  describes  an  experiment  in  which  he 
attached  a  mirror  to  a  magnetised  bar,  and  from 
this  mirror  a  beam  of  light  was  reflected  into  a 
theodolite.  This  was  the  first  example  of  making  a 
beam  of  light  act  as  a  weightless  pointer,  and  thus  to 
amplify  and  indicate  movement  upon  a  scale.  The 
method  has  been  of  the  greatest  service  to  physical 
science,  and  is  seen  to  perfection  in  the  arrangements 
of  Lord  Kelvin's  electrometer  and  galvanometer. 

Newton  established  that  white  light  consists  of 
innumerable  different  homogeneous  constituents  which 
are  dispersed  by  refraction.  This  is  proved  by  passing 
white  light  through  a  prism,  when  a  spectrum  is  pro- 
duced. The  index  of  refraction  becomes  greater  and 
greater  as  we  pass  through  red  to  orange,  orange  to 
yellow,  yellow  to  green,  green  to  blue,  blue  to  indigo, 
and  indigo  to  violet,  the  violet  rays  being  often  described 
as  the  most  refrangible  of  visible  rays.  It  is  also 
known  that  if  certain  media  are  placed  in  the  path  of 
the  beam  of  light,  and  the  light  is  then  passed  through 
a  prism,  certain  parts  of  the  spectrum  show  dark  bands, 
known  as  absorption  bands.  This  is  well  seen  when 
a  layer  of  blood  sufficiently  diluted  is  examined  with 
a  spectroscope.  Two  absorption  bands  may  then 
be  detected,  one  next  the  Frauenhofer  line  D, 
227 


HERMANN  VON  HELMHOLTZ 

narrower  than  the  other  and  blacker,  while  the 
broader  band  is  more  towards  the  right,  that  is,  nearer 
E.  The  remaining  part  of  the  spectrum  shows  all 
the  colours  with  beautiful  clearness.  The  analysis  of 
light  by  means  of  the  spectroscope  affords,  then,  a 
ready  means  of  examining  the  phenomena  of  absorp- 
tion, an  example  of  which  has  already  been  given  in 
treating  of  Helmholtz's  explanation  of  the  fact  that 
the  mixture  of  a  yellow  with  a  blue  pigment  produces 
green. 

The  peculiar  phenomenon  of  anomalous  disper- 
sion is  closely  associated  with  that  of  absorption. 
It  was  first  discovered  by  Fox  Talbot  about  1870.* 
The  experiment  of  Fox  Talbot  was  as  follows  : — '  I 
prepared  some  square  pieces  of  window  glass,  about  an 
inch  square.  Taking  one  of  these,  I  placed  upon  it  a 
drop  of  a  strong  solution  of  some  salt  of  chromium, 
which,  if  I  remember  rightly,  was  the  double  oxalate 
of  chromium  and  potash,  but  it  may  have  been  that 
substance  more  or  less  modified.  By  placing  a  second 
square  of  glass  on  the  first,  the  drop  was  spread  out  in 
a  thin  film,  but  it  was  prevented  from  becoming  too 
thin  by  four  pellets  of  wax  placed  at  the  corners  of 
the  square,  which  likewise  served  to  hold  the  two 
pieces  of  glass  together.  The  glasses  were  then  laid 
aside  for  some  hours  until  crystals  were  formed  in  the 
liquid.  These  were  necessarily  thin,  since  their  thick- 

1  Proc.  Roy.  Soc.  Edin.,  1870-71.  See  also  Tait  on  Light,  p.  156. 
Edinburgh,  1884. 

228 


HELMHOLTZ  IN  BERLIN 

ness  was  limited  by  the  interval  between  the  glasses. 
Of  course  the  central  part  of  each  crystal,  except  the 
smallest  ones,  was  bounded  by  parallel  planes,  but  the 
edges  were  bevilled  at  various  angles,  forming  so  many 
little  prisms,  the  smallest  of  them  floating  in  the  liquid. 
When  a  distant  candle  was  viewed  through  these 
glasses,  having  the  little  prisms  interposed,  a  great 
number  of  spectra  became  visible,  caused  by  the  in- 
clined edges.  Most  of  these  were  no  doubt  very 
imperfect,  but  by  trying  the  glass  at  various  points, 
some  very  distinct  spectra  were  met  with,  and  these 
could,  with  some  trouble,  be  isolated  by  covering  the 
glass  with  a  card  pierced  with  a  pin-hole.  It  was 
then  seen  that  each  prism  (or  oblique  edge  of  the 
crystal)  produced  two  spectra  oppositely  polarised  and 
widely  separated.  One  of  these  spectra  was  normal ; 
there  was  nothing  particular  about  it.  The  colours  of 
the  other  were  very  anomalous^  and,  after  many  experi- 
ments, I  came  to  the  conclusion  that  they  could  only 
be  explained  by  the  supposition  that  the  spectrum, 
after  proceeding  for  a  certain  distance,  stopped  short  and 
returned  upon  itself? 

The  words  italicised  show  that  Fox  Talbot  dis- 
covered the  real  nature  of  this  curious  phenomenon. 
Le  Roux,  in  1860,  had  found  that  vapour  of 
iodine,  which  allows  only  red  and  blue  rays  to  pass, 
refracts  the  red  more  than  the  blue,  the  opposite  of 
the  effect  of  a  glass  prism.  An  alcoholic  solution  of 
fuchsine  (an  aniline  colour)  gives  a  dark  absorption 
229 


HERMANN  VON  HELMHOLTZ 

band  in  the  green,  and  it  was  found  that  the  refrac- 
tive index  rises  (as  in  normal  bodies)  for  rays  from 
the  red  to  the  yellow.  But  all  the  rest  of  the 
transmitted  light,  consisting  of  the  more  refrangible 
rays,  is  less  refracted  than  the  red.  From  some 
experiments  of  De  Klecker,  published  in  1879,  it 
would  appear  that  c  The  addition  of  fuchsine  to  alcohol 
alters  the  speed  of  propagation  of  the  (so-called)  less 
refrangible  rays,  but  not  perceptibly  that  of  the  more 
refrangible.' * 

The  phenomenon  had  been  examined  by  many 
physicists  ;  but  the  explanations  were  unsatisfactory. 
Helmholtz's  first  solution  was  founded  on  the  sup- 
position that  in  transparent  media  certain  ponderable 
molecules  participate  in  the  vibrations  of  the  ether 
surrounding  them.  Mathematical  difficulties  arise  if 
we  suppose  that  there  is  discontinuity  between  the 
surfaces  of  these  particles  and  that  of  the  ether 
everywhere  in  contact  with  them,  so  he  further 
assumes  that  there  is  continuity,  that  is,  that 
there  is  no  abrupt  transition.  Now,  imagine  light 
falling  on  such  an  arrangement.  Part  of  the  vibra- 
tions transmitted  by  the  ponderable  molecules  is 
transformed  into  irregular  vibrations,  that  is  to  say, 
into  heat.  Thus  part  of  the  light  is  absorbed  or 
disappears.  The  ponderable  medium  opposes  to  the 
movement  of  the  vibrating  molecules  a  resistance  like 

1  Tait,  Light,  p.  157.  See  also  Jamin  et  Bouty,  Court  de  Physique,  t. 
iii.,  p.  542. 

230 


HELMHOLTZ  IN  BERLIN 

that  of  friction.  Each  molecule  of  the  ether  is  thus 
affected  by  ( I )  an  elastic  reaction  of  the  ether ; 
and  (2)  a  force  due  to  the  ponderable  medium, 
which  is  supposed  to  be  proportional  to  the  relative 
displacements  of  a  molecule  of  ether  and  a  molecule  of 
ponderable  matter.  The  ponderable  molecule,  on  the 
other  hand,  is  acted  upon  (i)  by  a  force  equal  to, 
and  in  the  reverse  direction  of,  the  preceding  ;  (2)  a 
force  due  to  the  neighbouring  ponderable  molecules  ; 
and  (3)  a  retarding  frictional  force  proportional  to 
the  rapidity  of  displacement.  These  conditions 
mathematically  expressed  lead  to  the  differential  equa- 
tions of  motion.  When  there  is  no  sensible  absorp- 
tion, the  formulae  indicate  a  normal  dispersion,  but 
when  great  absorption  takes  place,  theoretical  results 
are  obtained  in  accordance  with  those  observed  in 
anomalous  dispersion.  Thus,  as  expressed  by  Professor 
Tait,  Helmholtz's  explanation  'depends  upon  an 
assumption  as  to  the  nature  of  the  mutual  action 
between  the  luminiferous  ether  and  the  particles  of 
the  absorbing  medium,  coupled  with  a  farther  assump- 
tion connecting  the  absorption  itself  with  a  species  of 
friction  among  the  parts  of  each  absorbing  particle.' 
These  assumptions  were  first  suggested  by  Allenmeier, 
but  they  were  fully  applied  by  Helmholtz. 

This  explanation  was  offered  in   1874,  but  he  re- 
turned to  the  subject  in  1892  and  1893,  and  endeavoured 
to   account   for   the   fact  in  accordance  with    Clerk 
Maxwell's  electro-magnetic    theory  of  light,  by  the 
231 


HERMANN  VON  HELMHOLTZ 

conception  of  pairs  of  oppositely  charged  particles 
(ions)  of  inert  matter  fixed  in  the  ether.  This  paper 
probably  contributed  more  to  supporting  the  electro- 
magnetic theory  of  light  than  to  an  adequate  ex- 
planation of  anomalous  dispersion,  which  is  an  easily 
demonstrable  fact  still  incapable  of  explanation. 

It  was  in  1873  and  1874  that  Helmholtz  wrote  two 
important  papers  on  the  Optical  Principles  of  the 
Compound  Microscope,  and  determined  the  limits  of 
amplification.  This  was  accomplished  independently 
of  similar  and  even  more  elaborate  work,  both  mathe- 
matical and  experimental — carried  out  by  the  greatest 
living  authority  on  all  such  questions,  Professor  Abbe  of 
Jena,  to  whose  researches,  especially  in  connection  with 
the  construction  on  correct  principles  of  apochromatic 
lenses,  science  owes  so  much.  Helmholtz,  in  the  first 
place,  established  a  formula  by  which  we  can  express 
the  ratio  of  the  linear  magnitudes  of  the  object  and  its 
image,  in  terms  of  the  divergence  of  the  rays  before 
and  after  refraction,  which  is  independent  of  the 
distance  of  the  focal  lengths  of  the  refracting  surface.1 
He  showed  also  how  to  measure  and  define  the 
angle  of  aperture,  and  finally  proved  that  in  conse- 
quence of  the  dispersion  of  light  at  the  edges  of 
minute  bodies,  no  objects  can  be  seen  that  are  smaller 
than  the  -g^V^h  of  a  millimetre,  that  is,  the  y^s^oo^ 
of  an  inch.  So  far  the  microscope  can  go  and  no  farther. 

1  Heath's  Geometrical  Optics,  p.  56. 


232 


CHAPTER     XVI 

HELMHOLTZ    IN    BERLIN PHYSICAL    RESEARCHES 

CONTINUED 

6.   On  the  Principles  of  Dynamics. 

T  N  his  later  years,  Helmholtz  was  much  occupied 
-*-  with  the  discussion  of  dynamical  questions  of 
the  most  abstruse  nature.  To  him  all  physical 
phenomena  were  ultimately  to  be  explained  on 
dynamical  principles,  not  merely  those  evident  to 
the  senses,  but  those  in  the  greater  world  of  mole- 
cular action.  His  mental  vision  penetrated  below  the 
surfaces  of  things,  and  to  such  a  mind  the  mazy  dances 
and  whirls  of  atoms  were  ruled  as  rigidly  by  dynami- 
cal laws  as  were  the  movements  of  the  planetary  bodies. 
It  was  also  characteristic  of  his  mental  capacities  that 
they  seemed  to  increase  in  power  as  time  went  on. 
In  his  old  age  he  was  not  satisfied  merely  with  the 
contemplation  of  what  he  had  done,  although  that  of 
itself  must  have  been  a  source  of  supreme  satisfaction, 
nor  did  he  rest  merely  on  his  experience  of  men  and 
things,  but  he  was  ever  passing  into  higher  regions  of 
thought.  Here  he  was  engaged,  not  in  the  gathering 
233 


HERMANN  VON  HELMHOLTZ 

of  facts,  but  in  the  establishment  of  great  principles, 
which  would  be  applicable  to  abstract  dynamics, 
hydrodynamics,  thermodynamics,  electrodynamics, 
alike,  and  by  which  insight  might  be  obtained  into 
hidden  processes.  In  1884  we  find  three  elaborate 
mathematical  papers  on  what  he  termed  monocyclic 
systems;  in  1886,  a  paper  on  the  principle  of  least 
action  ;  in  1887,  another  on  the  same  subject ;  and  in 
1892,  a  third  paper  on  the  principle  of  least  action  in 
electrodynamics. 

Cyclic  systems  are  those  in  which  there  are  periodic 
or  circulating  motions.  This  is  a  somewhat  vague 
description,  but  it  may  indicate  what  is  meant.  A 
motion  definable  by  a  single  co-ordinate,  like  that 
of  a  circular  disc  spinning  round  its  axis,  he  termed 
monocyclic,  but  he  also  conceived  the  more  com- 
plicated case  of  a  polycyclic  system  definable  by 
a  large  number  of  co-ordinates,  satisfying  certain 
assumed  conditions.  The  position  of  a  disc  in  a 
monocyclic  system  depends  on  the  angle  which  a 
plane  containing  the  axis  tmakes  with  a  plane  fixed 
in  space ;  but  the  energy  depends  on  the  angular 
velocity.  The  potential  energy  remains  unaltered 
while  the  disc  revolves.  The  broad  lines  of  the 
methods  by  which  such  systems  may  be  investi- 
gated were  first  laid  down  by  Thomson  (Lord 
Kelvin)  and  Tait.  Helmholtz  narrowed  the  dis- 
cussion to  certain  types  of  such  systems.  He 
assumes  for  such  that  neither  the  kinetic  nor  the 
234 


HELMHOLTZ  IN  BERLIN 

potential  energy  depend  on  the  uncontrollable  co- 
ordinates themselves  (that  is,  co-ordinates  incapable 
of  being  affected  by  the  action  of  any  external 
system),  but  only  on  the  velocities  corresponding 
to  them.  Further,  he  assumes  that  the  velocities 
corresponding  to  the  controllable  co-ordinates  are 
always  very  small  in  comparison  with  the  others, 
and  further,  that  the  accelerations  of  the  uncontrollable 
or  cyclic  velocities  are  also  small.  These  assumptions 
imply  that  no  forces  depend  on  the  cyclic  co-ordinates. 
Changes  in  the  cyclic  velocities  may  change  the  energy 
of  the  system,  but  changes  in  the  cyclic  co-ordinates 
cannot  do  so.1  Helmholtz  also  studied  the  effects  of 
one  monocyclic  system  on  a  neighbouring  one,  and  of 
two  or  more  monocyclic  systems  held  together  by  a 
common  band.  The  chief  interest  of  these  investiga- 
tions arises  from  the  fact,  that  thermodynamic  pheno- 
mena (more  especially  those  related  to  the  second  law) 
show  the  peculiarities  of  monocyclic  systems.  One 
may  also  say  that  the  value  of  the  work  of  Helm- 
holtz in  this  department  is,  that  his  conceptions  of 
monocyclic  and  polycyclic  systems  have  such  general 
application. 

Helmholtz  showed  that  the  principle  of  least  action 
enunciated  in  1744  by  Maupertuis,  and  expanded  by 
William  Rowan  Hamilton,  the  inventor  of  quaternions, 
is  even  a  greater  and  more  comprehensive  generalisa- 

1  For  a  discussion  of  these  difficult  matters,  see  Gray,  Treatite  on 
Electricity  and  Magnetism,  vol.  i.,  chap.  7,  p.  180. 

235 


HERMANN  VON  HELMHOLTZ 

tion  than  that  of  the  law  of  the  conservation  of  energy. 
This  law  is  not  of  itself  sufficient  to  give  a  dynamical  ex- 
planation of  the  mutual  actions  or  relations  of  a  system. 
The  principle  of  least  action,  however,  gives  a  dyna- 
mical process  from  which,  with  certain  assumptions, 
those  relations  can  be  deduced.  Maupertuis,  who  was 
a  contemporary  of  Voltaire,  and  one  of  the  brilliant 
group  of  men  gathered  around  him  by  Frederick  the 
Great,  saw  in  his  principle  an  indubitable  proof  of  the 
existence  of  God,  but  he  was  not  able  to  give  it  a 
mathematical  form,  nor  could  he  have  foreseen  how 
important  it  was  destined  to  become  in  general  dyna- 
mics. For  a  long  period  it  was  only  a  metaphysical 
conception,  even  although  mathematicians  of  the 
first  rank  endeavoured  to  express  it  in  the  language 
of  dynamics. 

The  subject  has  been  fully  treated,  without  the  aid 
of  formulae  that  are  bewildering  to  the  uninitiated, 
by  Professor  Leo  Koenigsberger,  in  his  admirable 
address  on  the  Researches  of  Helmholtz  in  Mathe- 
matics and  Mechanics,  delivered  in  1895,  the  year 
after  the  decease  of  Helmholtz. I 

Descartes  founded  analytical  geometry,  which,  by 
determining  the  distances  of  all  points  by  fixed  lines, 
or  co-ordinates,  reduced  spatial  relations  to  their  arith- 
metical expression,  and  by  the  use  of  algebraic 

1  Rede  zum  Geiurtsfeste  des  Kochitteligen   Grossherzogs   Karl  Friedrich 
und  zur  akademhchen  Preis-vertheilung,  am  22  Nov.   1895,  von  Dr  Leo 
Koenigsberger,  Professor  der  Mathematik.      Heidelberg,  1895. 
236 


HELMHOLTZ  IN  BERLIN 

equations  solved  geometrical  problems,  and  demon- 
strated geometrical  propositions.  Descartes's  error  in 
theoretical  physics  was  in  conceiving  matter  as  moved 
only  by  impulsion  and  pressure,  and  not  by  internal 
forces  ;  but  he  recognised  that  the  quantity  of  matter 
and  motion  in  the  universe  remained  unchanged.  He 
also  defined  the  quantity  of  motion  as  being  equal 
to  the  product  of  mass  and  speed  (in  v).  The  next 
great  name  in  this  arena  of  thought  is  Leibnitz,  who, 
about  the  same  time  as  Newton  was  engaged  on 
establishing  the  differential  calculus  or  calculus  of 
fluxions.  He  argued  that  it  was  rather  the  quantity 
of  vis  that  remained  unchanged  in  the  universe,  and 
he  defined  this  quantity  as  the  product  of  the  mass 
and  the  square  of  the  speed  (m  <y2).  The  two  views 
led  to  a  schism  among  thinkers,  some  supporting 
Descartes,  among  those  Euler,  while  others  were  on 
the  side  of  Leibnitz.  Kant  admitted  the  Leibnitzian 
view  with  a  limitation.  It  is,  however,  wholly  a 
question  of  definition  and  of  nomenclature.  If  we 
mean  by  a  force,  a  cause  proportionate  to  the  quantity 
of  motion  of  a  body,  the  Cartesian  principle  applies  ; 
but  if  we  mean  by  force,  the  power  of  a  body  to 
overcome  a  continuous  and  uniform  resistance,  the 
formula  of  Leibnitz  holds  good,  namely,  that  the 
work  performed  by  the  force  is  equal  to  the  pro- 
duct of  half  the  mass  into  the  difference  of  the 
squares  of  the  speeds  at  the  commencement  and  at 
the  end  of  the  motion.  Both  principles  were  recog- 
237 


HERMANN  VON  HELMHOLTZ 

nised  by  Newton  ;  and  in  the  language  of  the  present 
day  m  v  (mass  into  speed)  is  the  quantity  of  motion 
or  momentum,  and  m  v2  (mass  into  square  of  speed) 
is  twice  the  kinetic  energy. 

From  a  consideration  of  the  principles  of  the  lever, 
the  pulley  and  the  inclined  plane,  came  the  definition 
of  work  as  the  product  of  the  quantity  of  a  force  into 
the  minute  movement  of  a  material  point  measured  in 
the  direction  of  the  force.  This  led  to  the  establish- 
ment of  the  principle  of  virtual  velocities  according 
to  which  any  material  system  is  in  equilibrium  only 
when  for  every  virtual  or  infinitely  small  movement 
compatible  with  the  connections  of  the  points,  the 
work  of  the  entire  system  is  equal  to  zero.  From 
Galileo's  doctrine  of  inertia,  and  the  enunciation  of 
Newton's  three  laws  of  motion,  a  basis  was  formed  for 
theoretical  dynamics.  The  more  important  of  these 
laws  in  the  present  connection  are  the  first  and  second. 
The  first  asserts  that  every  body  continues  in  a  state 
of  rest  or  of  uniform  motion  in  a  straight  line,  unless 
compelled  to  change  that  state  by  the  action  of  some 
external  force  ;  in  other  words,  it  expresses  the  prin- 
ciple of  inertia.  Force  may  be  defined  as  that  which 
changes  or  tends  to  change  the  state  of  rest  or  motion 
of  a  body,  and  force  is  measured  by  the  change  of 
momentum  it  produces  in  a  unit  of  time.  In  the  idea 
of  momentum,  the  quantity  of  matter  moved  (mass) 
is  taken  into  account  as  well  as  the  rate  at  which  it 
travels.  This  leads  to  the  second  law.  Rate  of 


HELMHOLTZ  IN  BERLIN 

change  of  momentum  is  proportional  to  the  impressed 
force,  and  takes  place  in  the  direction  in  which  the 
force  acts.  Then  we  have  the  third  law,  that  to 
every  action  there  is  always  an  equal  and  opposite 
reaction. 

Greater  precision  is  introduced  by  adopting  the 
Gaussian  notion  of  unit  force.  If  a  unit  of  force 
act  for  a  unit  of  time  upon  a  unit  of  mass,  the 
velocity  of  the  mass  will  be  changed,  and  the  total 
acceleration  will  be  unity  in  the  direction  of  the 
force.  Further,  in  accordance  with  Newton's  Second 
Law,  the  magnitude  and  direction  of  this  total 
acceleration  will  be  the  same  whether  the  body  is 
originally  at  rest  or  in  motion.  Again,  when  any 
number  of  forces  act  on  a  body,  the  acceleration 
due  to  each  force  is  the  same  in  direction  and  magni- 
tude as  if  the  others  had  not  been  in  action.1 

It  was  about  this  stage  that  Huygens,  Leibnitz, 
and  the  Bernoullis  contributed  to  the  discussion, 
but  their  arguments  were  often  of  a  metaphysical 
character. 

Half  the  product  of  the  mass  of  a  particle  into 
the  square  of  its  speed  is  its  kinetic  energy.  A 
material  system  may  have  any  number  of  such  par- 
ticles, and  the  sum  of  the  individual  kinetic  energies 
will  become  the  kinetic  energy  of  the  system. 
Further,  any  increase  in  the  kinetic  energy  of  a 
material  system  in  passing  from  one  configuration 

1  Clerk  Maxwell,  Matter  and  Motion,  p.  42.     London,  1876. 
239 


HERMANN  VON  HELMHOLTZ 

into  another  is  equal  to  the  work  done  on  the 
system  by  the  external  forces.  If  these  forces 
depend  upon  positions  and  mutual  distances  of  the 
particles,  the  system,  after  a  change  from  one  con- 
figuration into  another,  and  a  return  to  its  original 
condition,  will  suffer  no  change  in  kinetic  energy. 
Such  a  system  is  described  as  conservative.  When 
a  conservative  system,  in  its  change  from  one  con- 
figuration into  another,  does  a  certain  amount  of 
work,  then  its  power  of  doing  work  in  virtue  of 
its  configuration,  or,  in  other  words,  its  potential 
energy,  is  greater  in  the  first  position  than  in  the 
second. 

In  this  way  we  arrive  at  a  statement  of  the  law  of 
the  constancy  of  energy,  which  asserts  that,  in  the 
motions  of  any  conservative  system,  the  sum  of  the 
potential  and  of  the  kinetic  energy  is  unchangeable. 
This,  of  course,  implies  the  impossibility  of  the  per- 
petual motion,  or  the  production  of  work  from 
nothing,  because  if  it  (the  perpetual  motion)  were 
possible,  we  might  gain  work  by  changing  the 
system  one  way  and  then  back  again  by  a  different 
route  to  its  original  condition.  This  principle  of 
conservation  was  long  recognised  in  a  limited  sense, 
but  it  did  not  seem  to  apply  to  all  kinds  of  forces. 
Thus,  if  a  system  moves  backwards  and  forwards 
on  the  same  track,  first  without  and  afterwards  with 
friction,  then  the  friction  in  the  latter  case  will 
diminish  the  velocity,  and  there  will  be  a  loss  of 
240 


HELMHOLTZ  IN  BERLIN 

kinetic  energy.  Consequently  we  must  extend  the 
conception  of  energy  from  that  of  potential  energy, 
or  the  energy  of  position,  so  as  to  include  the  energy 
of  motion,  which  may  appear  as  heat  or  other  forces. 
The  loss  of  kinetic  energy  in  the  above  case  will  then 
be  equal  to  the  amount  of  heat  produced.  This  idea 
led  Mayer  (see  p.  47)  to  the  fundamental  conception 
of  the  equivalence  of  heat  and  mechanical  work,  and 
it  no  doubt  also  guided  Helmholtz  in  writing  his  tract, 
Die  Erhaltung  der  Kraft.  The  outcome  of  this  dis- 
cussion is  that  the  work  done  by  any  conservative 
system  in  changing  from  one  configuration  into 
another,  depends  on  the  configurations  at  the  be- 
ginning and  the  end  of  the  process,  and  not  on  the 
intermediate  stages.  The  tract  was  intended  to  show 
the  theoretical  and  practical  importance  of  the  law 
of  the  constancy  of  energy,  not  from  a  priori  con- 
siderations, but  by  induction  from  facts,  and  especially 
from  vain  attempts  to  discover  or  invent  the  per- 
petual motion.  It  does  not  tell  us  anything  about 
the  mode  by  which  the  configuration  is  changed,  or, 
to  put  the  matter  in  other  words,  it  does  not  define 
the  route  followed  by  the  system  in  passing  from  the 
first  configuration  into  the  last. 

The  publication  of  this  tract,  which  has  had  so 
great  an  influence  on  science,  was  often  referred  to 
in  later  years  by  Helmholtz.  It  was  therefore  fitting 
that  he  should  crown  the  edifice  he  had  reared  by 
the  great  papers  of  his  later  years,  in  which  he  re- 
ft 


HERMANN  VON  HELMHOLTZ 

turned,  with  mature  powers  and  with  the  enormous 
experience  gained  in  many  fields  of  physiological 
and  physical  research,  to  the  problems  of  his  early 
youth.  As  already  explained,  the  notion  of  action 
at  a  distance  was  gradually  but  completely  abandoned, 
and  its  place  was  taken  by  that  of  a  medium 
connecting  masses  of  matter  with  each  other,  and 
transmitting  force.  But  if  this  new  conception  is 
still  mechanical,  if  particles  of  matter  are  straining 
upon  the  invisible  ties  that  bind  them  together,  if 
all  attractions  and  repulsions  occur  in  the  medium 
known  as  the  ether,  what  is  the  simplest  expression 
of  the  laws  that  control  these  dynamical  operations  ? 
Can  any  general  principle  be  established  by  which, 
and  even  without  experiment,  these  dynamical  opera- 
tions can  be  deductively  explained  ?  It  was  felt  by 
many  that,  even  with  the  help  of  Galileo's  notion 
of  inertia  and  Newton's  laws,  some  mechanical  con- 
ceptions, such  as  statical  equilibrium,  or  the  theory 
of  virtual  velocities,  were  not  fully  proved  ;  while,  on 
the  other  hand,  many  phenomena,  molecular,  chemi- 
cal, electrical,  magnetical,  were  hidden  from  direct 
observation  and  immediate  experience.  The  enuncia- 
tion of  the  law  of  the  conservation  of  energy  changed 
the  aspect  of  affairs,  and  gave  a  great  impulse  to  the 
development  of  theoretical  dynamics.  The  notion 
of  force  fell  into  the  background,  while  mass  and 
energy  became  recognised  as  indestructible  quantities. 
Energy  was  twofold  :  kinetic  energy  depended  in  all 
242 


HELMHOLTZ  IN  BERLIN 

cases  on  the  speeds  of  the  moving  masses  ;  potential 
energy  by  the  positions  of  the  masses  in  any  system. 
The  discussion  of  the  different  modes  of  energy,  and 
the  conditions  of  the  passage  of  one  mode  of  energy 
into  another,  became  the  subject-matter  of  physics 
and  chemistry.  Helmholtz  did  not,  as  had  hitherto 
been  done,  deduce  the  general  principles  of  mechanics 
from  equations  of  motion,  but  he  started  from  a  more 
general  principle,  that  of  least  action.  The  papers  on 
this  subject  are,  according  to  Hertz,  the  high-water 
mark  of  modern  physics. 

Action,  according  to  Leibnitz,  was  the  product  of 
the  mass,  the  distance  through  which  it  was  moved, 
and  the  speed.  In  other  words,  the  product  of  the 
vis  viva  (twice  the  kinetic  energy),  and  the  time. 
According  to  this  view,  when  a  body  passed  from 
one  configuration  into  another,  the  total  amount  of 
the  action  had  a  limit  value,  while  the  amount  of 
the  energy  remained  unchanged.  The  element  of 
time  came  into  the  statement,  so  that  the  position 
of  individual  parts  of  the  system  at  specific  times 
during  the  whole  time  occupied  by  the  change  of 
configuration  could  also  be  taken  into  account. 
Lagrange  and  Hamilton  also  introduced  the  idea, 
that,  while  the  relative  amount  of  potential  and 
kinetic  energy  were  constantly  changing,  the  amount 
of  this  change  must  also  be  considered ;  while 
Jacobi,  assuming  that  the  potential  energy  is  inde- 
pendent of  time,  gave  the  kinetic  energy  a  certain 
243 


HERMANN  VON  HELMHOLTZ 

value,  and  thus  eliminated  the  increment  of  time 
from  the  action.  Hamilton  stated  the  principle  of 
least  action  in  yet  another  form.1  He  showed  that 
the  complete  solution  of  any  kinetical  problem,  as 
regards  the  action  of  any  conservative  system  of 
forces  and  constraint  depending  on  the  reaction  of 
smooth  surfaces  or  curves,  is  reducible  to  the  deter- 
mination of  a  single  quantity,  which  he  called  the 
characteristic  function  of  the  motion.  This  quantity 
is  found  from  a  partial  differential  equation  of  the 
first  order  and  second  degree,  and  from  the  com- 
plete integral  of  this  equation  all  the  circumstances 
of  the  motion  may  be  deduced  by  differentiation. 
This  has  been  called  the  method  or  principle  of 
varying  action.2 

The  principle  of  least  action  may  be  thus  briefly 
stated  : — Given  a  conservative  system  in  any  con- 
figuration, and  different  paths  by  which  it  could  be 
guided  to  any  other  definite  configuration,  under  the 
condition  that  the  sum  of  its  potential  and  kinetic 
energies  is  constant,  then  the  path  for  which  the 
action  is  least  is  the  one  along  which  the  system 
would  move  unguided  if  the  proper  initial  velocities 
were  given  to  it.  The  term  action*  as  applied  to  a 

'  W.  R.  Hamilton  on  a  General  Method  of  Dynamics.  Phil.  Trans. 
1834,1835. 

2  Thomson  and  Tail's  Natural  Philosophy,  vol.  i.,  pt.  insect.  333  ;  also 
Tait  on  the  Application  of  'Hamilton 's  Characteristic  Function  to  Special  Cases 
of  Constraint.  Trans.  Roy.  Sec.  Edin.,  vol.  xxiv.,  and  Scientific  Papers,  vol. 
i.,  p.  54. 

244 


HELMHOLTZ  IN  BERLIN 

moving  system  for  a  short  interval  of  time,  is  usually 
defined  as  the  product  of  double  the  average  kinetic 
energy  during  that  time,  multiplied  by  the  time  ;  or, 
shortly,  it  is  double  the  time-integral  of  the  kinetic 
energy.  Discussions  based  on  this  definition  give  the 
action  in  terms  of  the  initial  and  final  co-ordinates  of 
the  system  and  the  time  prescribed  for  the  motion. 
Again,  action  may  be  expressed  in  another  way,  as 
the  sum  of  the  products  of  the  average  momentum 
for  the  spaces  through  which  particles  move,  multi- 
plied by  the  length  of  the  spaces.  For  double  the 
kinetic  energy  during  a  short  interval  of  time  multi- 
plied by  the  time,  is  equal  to  the  average  momentum 
during  that  time  multiplied  by  the  space  described. 
Investigations  on  the  second  definition  of  action 
give  the  action  in  terms  of  the  initial  and  final 
co-ordinates  of  the  system,  and  the  constant  sum 
of  the  potential  and  kinetic  energies.1 

It  is  not  easy  finding  simple  examples  of  the  appli- 
cation of  the  principle  ;  nor  can  it  be  said  that  the 
fundamental  dynamic  significance  of  the  principle  has 
been  made  clear.  Quantities  like  velocity,  momentum, 
kinetic  energy,  potential  energy,  are  what  might  be 
called  instantaneous  properties  of  a  system.  Their 
values  are  definite  at  each  instant,  and  can  be  assigned 
without  reference  to  what  has  taken  place  previously. 
But  the  Action  of  a  system  at  any  instant  depends  on 

1  Thomson  and  Tait,  Natural  Philosophy,  vol.  i.,  part  i.,  sec.  326  to 
368,  pp.  337-439- 

245 


HERMANN  VON  HELMHOLTZ 

the  previous  history,  reckoning  from  some  chosen 
instant,  as  epoch.  If  we  take  the  simplest  case  of  a 
particle  moving  with  constant  velocity,  and  therefore 
with  constant  kinetic  energy  in  a  straight  line,  the 
Action  is  simply  the  kinetic  energy  multiplied  by  the 
time,  and  increases  at  a  steady  rate.  If  the  particle  is 
guided  between  two  positions  by  any  other  than  the 
straight  line  connecting  these  positions,  it  must  describe 
a  longer  course  and,  since  the  speed  is  constant,  take  a 
longer  time.  In  this  simplest  of  all  cases  the  minimum 
property  is  obviously  fulfilled  when  the  path  pursued 
is  the  natural  path. 

As  already  indicated,  the  principle  of  least  action, 
taken  in  connection  with  the  principle  of  the  con- 
stancy of  the  sum  of  the  potential  and  kinetic  energies, 
leads  to  the  equations  of  motion  of  the  system  under 
consideration.  But  it  is  only  in  problems  of  abstract 
dynamics  that  the  sum  of  the  potential  and  kinetic 
energies  is  constant.  With  the  recognition  of  the 
true  nature  of  heat  came  the  great  modern  generalisa- 
tion of  the  conservation  of  energy.  Heat  is  a  form 
of  molecular  and  ethereal  energy  ;  and  dynamically 
this  great  doctrine  of  the  conservation  of  energy  is 
the  earlier  principle  of  the  constancy  of  the  potential 
and  kinetic  energies,  if  cognisance  be  taken  of  the 
invisible  motions  of  molecules  and  ether  as  well  as  of 
the  visible  mass  motions. 

The  idea  of  Helmholtz  was  to  apply  the  principle 
of  action  to  these  wider  problems.  In  the  general 
246 


HELMHOLTZ  IN  BERLIN 

dynamical  system  considered  by  him,  the  internal 
forces  are  assumed  to  be  conservative,  but  the  external 
forces  depend  on  the  time  and  work  done  by  them  and 
can  be  specially  calculated. 

Helmholtz  based  his  investigations  on  two  functions 
of  the  co-ordinates  and  the  velocities,  namely,  Hamil- 
ton's Principal  Function,  and  the  total  energy.  The 
total  energy  is  the  sum  of  the  potential  and  kinetic 
energies,  while  the  Principal  Function  (called  by 
Helmholtz  the  Kinetic  Potential]  is  the  difference  of 
these  two  quantities.  The  principle  of  least  action 
was  then  defined  in  these  words  : — If  calculated  for 
equal  short  intervals  of  time,  the  negative  mean  value 
of  the  kinetic  potential,  while  the  system  passes  by  its 
natural  path  from  one  configuration  to  another,  is  a 
minimum  as  compared  with  its  value  by  all  other 
contiguous  paths  described  in  the  same  time  from  the 
initial  to  the  final  configuration.  For  cases  of  equili- 
brium, the  kinetic  potential  becomes  the  potential 
energy  ;  and  the  principle  just  enunciated  becomes 
the  well-known  condition  for  stable  equilibrium, 
namely,  the  potential  energy  must  be  a  minimum. 
From  the  minimum  theorem  of  the  kinetic  potential, 
Helmholtz  then  deduced  the  principle  of  the  constancy 
of  energy,  and  applied  the  principle  to  important 
general  problems  in  thermodynamics  and  electro- 
dynamics. He  considered  that  the  truth  of  the 
principle  went  far  beyond  the  dynamics  of  ponderable 
masses,  and  that  it  was  the  general  law  for  all  reversible 
247 


HERMANN  VON  HELMHOLTZ 

processes  in  nature  ;  while,  in  regard  to  irreversible 
processes — as,  for  example,  in  the  generation  and  con- 
duction of  heat — the  irreversibility  appeared  to  depend, 
not  upon  the  essential  nature  of  things,  but  upon  the 
limitation  of  our  powers  in  reducing  to  order  again 
haphazard  motions  of  molcules,  or  in  reversing  the 
molecular  movements  associated  with  the  transference 
of  heat. 

The  outcome  of  this  discussion  is  to  show  that  in 
the  mechanical  operations  of  nature,  there  is  simplicity 
and  economy.  The  members  of  a  system,  free  to 
move  amongst  each  other,  and  unaffected  by  any 
external  system,  may  have  many  paths  along  which 
they  might  pass  from  one  position  to  another,  so  as 
to  make  a  change  from  one  configuration  to  another, 
but  they  always  travel  by  the  best  possible  route,  and 
thus  bring  about  the  change  in  a  simple  way.  What 
the  real  significance  of  this  is  we  do  not  know,  and 
we  must  eliminate  from  the  conception  the  notion  of 
choice.  It  may  yet  be  shown  why  this  must  be  so. 
This  principle,  apparently,  has  universal  application, 
and  it  is  the  guide  in  many  investigations. 

In  his  paper  on  Maxwell's  theory  of  movements  in 
the  free  ether,  already  referred  to  (p.  219),  Helmholtz 
plunges  into  questions  of  an  extremely  difficult  nature, 
and  on  which  all  his  powers  of  mathematical  analysis 
and  his  capacity  of  wielding,  like  an  intellectual  Titan, 
the  tremendous  principles  of  the  conservation  of  energy 
and  of  least  action,  are  brought  to  bear.  Ponderable 
248 


HELMHOLTZ  IN  BERLIN 

matter  is  everywhere  bathed  by  ether  and  is  permeated 
by  it.  If  the  ponderable  matter  and  the  ether  are  in 
close  grip  one  with  the  other,  one  may  reason  from  the 
movements  of  the  former  to  those  of  the  latter.  But 
if  we  consider  the  spaces  which  are  empty  of  ponder- 
able bodies  and  filled  with  ether  alone,  then  the 
question  arises,  has  the  ether  any  inertia  ?  Again, 
suppose  ponderable  bodies  move  in  the  ether,  can  the 
latter  get  out  of  their  way,  or  does  it  pass  through 
the  ponderable  bodies  like  water  through  a  sieve,  or 
does  the  ether  remain  at  rest  or  is  it  partly  dragged 
along  by  the  ponderable  bodies  ?  Helmholtz  finds, 
on  the  assumption  that  ether  is  an  incompressible 
frictionless  fluid,  having  no  inertia,  that  the  electro- 
magnetic law  of  Clerk  Maxwell,  experimentally 
proved  by  Hertz,  holds  good,  and  explains  all  the 
phenomena.  He  finally  draws  important  conclusions 
as  to  the  character  of  the  discontinuity  at  the 
boundary  of  ether  and  ponderable  matter,  and  the 
manner  in  which  the  electrical  and  magnetic  forces 
originate.  This  paper  was  a  fitting  termination  to 
the  labours  of  Helmholtz  in  the  lofty  region  of 
mathematical  physics. 


249 


CHAPTER    XVII 

THE    PHILOSOPHICAL   POSITION    OF    HELMHOLTZ 

TO  understand  the  position  of  Helmholtz,  with 
regard  to  the  great  questions  in  philosophy, 
we  must  take  into  account  the  school  in  which  he 
was  trained  and  the  path  which  he  chose  for  himself  in 
physiological  investigation.  No  physiological  principle 
influenced  him  so  much  as  that  of  the  specific  energy 
of  nerves,  taught  by  Johannes  Miiller.  The  statement 
of  this  principle  is,  that  in  whatever  way  a  terminal 
organ  of  sense  may  be  stimulated,  the  result  in  con- 
sciousness is  always  of  the  same  kind.  Thus  the 
vibrations  of  the  ether  that  constitute  physical  light, 
or  pressure,  or  electrical  stimulation,  all  cause,  when 
applied  to  the  retina  or  to  the  optic  nerve,  sensations 
of  luminosity.  The  same  is  true  of  all  the  sense 
organs.  It  is  evident,  therefore,  that  there  is  no 
correspondence  between  the  sensation  and  the  physical 
nature  of  the  stimulus  arousing  it,  seeing  that  the 
latter  may  be  varied  while  the  former  remains  un- 
altered. This  principle  was  the  guide  to  Helmholtz 
in  all  his  physiological  work  on  the  senses,  just  as  that 
250 


HIS  PHILOSOPHICAL  POSITION 

of  the  conservation  of  energy  controlled  and  directed 
him  in  the  sphere  of  physical  research.  Lotze  has 
finely  said,  that  philosophy  is  always  a  piece  of  life,  and 
that  a  prolonged  philosophical  labour  is  nothing  else 
but  the  attempt  to  justify,  scientifically,  a  fundamental 
view  of  things  which  has  been  adopted  in  early  life.1 
This  is  well  illustrated  in  the  case  of  Helmholtz. 

He  early  adopted  a  system  of  empiricism,  and  was 
thus,  in  a  modified  sense,  a  follower  of  John  Locke,  the 
English  philosopher  who  denied  the  existence  of  innate 
ideas.  Nothing  is  in  the  intellect  except  what  came 
by  sensory  impressions,  and,  to  begin  with,  the  mind 
was  a  tabula  rasa,  a  blank  tablet,  ready  to  receive  the 
inscriptions  of  the  outer  world.  Knowledge  was 
derived  from  sensuous  perception,  or  sensation,  and 
partly  from  internal  perception  or  reflection.  Ex- 
ternal objects  were  appreciated  by  the  senses,  while 
within  there  was  the  apprehension  of  psychical 
phenomena  by  a  kind  of  internal  sense.  All  spatial 
properties  had  objective  reality,  but  sensible  qualities, 
such  as  sound,  colour,  taste,  were  in  the  perceiver  and 
not  in  the  objects  themselves.  Sensations  were  signs 
or  symbols,  not  copies  of  the  external  things.  They 
are  no  more  like  the  real  thing  than  words  are  like 
the  ideas  they  represent.  In  the  inner  world  of  mind 
reflection  enables  us  to  know  the  actions  of  our 
willing  and  thinking  faculties.  From  the  two 

1  Philosophy  of  the  Last  Forty  Years.  Contemporary  Re-view,  Jan. 
1880. 

251 


HERMANN  VON  HELMHOLTZ 

sources  of  knowledge,  the  internal  and  external,  we 
obtain  ideas,  which  may  be  simple  or  complex,  and 
ideas  always  deal  with  modes,  substances  or  relations. 
It  is  clear,  therefore,  that  our  knowledge,  accord- 
ing to  these  doctrines,  must  be  mainly  gained  from 
experience. 

Spinoza,  Descartes  and  Leibnitz,  on  the  other 
hand,  held  that  the  mind,  by  its  own  powers,  could 
transcend  the  limits  of  experience  and  reach  the  truth. 
The  pantheistic  monism  of  Spinoza  implied  unity  of 
substance,  this  substance  having  the  fundamental 
qualities  of  thought  and  extension  ;  God,  ourselves,  and 
the  world  were  one.  A  mode  of  extension  (an  ex- 
ternal object),  and  the  idea  of  an  object  are,  in  the 
language  of  Spinoza,  the  same  thing  expressed  in 
two  different  ways.  To  understand  a  sensory  im- 
pression we  must  have  an  idea  of  the  affected  as 
well  as  of  the  affecting  body. 

Descartes  conceived  all  external  bodies  to  be  ex- 
tended substances,  while  the  soul  is  a  thinking  sub- 
stance without  extension.  External  bodies  are  real, 
because  we  are  conscious  of  the  dependence  of  sensa- 
tions on  external  causes.  Soul  and  body  interact, 
touching  at  one  point,  the  pineal  gland,  and  thus 
body  and  spirit  constitute  a  dualism,  but  the  mode 
of  interaction  is  incomprehensible.  Why  did  Des- 
cartes attach  such  importance  to  an  obscure  little 
organ,  now  known  to  be  an  abortive  eye  ?  Leibnitz 
introduced  his  strange  system  of  monads, — a  monad 
252 


HIS  PHILOSOPHICAL  POSITION 

being  a  simple  unextended  system,  having  power 
of  action.  Active  force  is  the  essence  of  substance. 
Monads  are  like  the  atoms  of  Democritus,  they 
are  centres  of  force,  a  notion  not  unlike  the  modern 
conception  of  Lord  Kelvin,  which  describes  atoms 
as  rotational  movements  of  the  ether.  But  we  part 
company  with  modern  notions  when  we  meet  with 
the  assertion  of  Leibnitz,  that  the  active  forces  in 
monads  are  ideas.  The  soul  is  a  monad,  for  it  can 
act  on  itself,  a  proof  of  its  substantiality.  Every 
finite  monad  has  a  perception  of  those  parts  of  the 
universe  to  which  it  is  related  ;  to  our  sensory  per- 
ceptions, the  order  of  the  monads  appears  as  the 
temporal  and  spatial  order  of  things,  while  time  is 
the  order  of  succession  of  phenomena.  There  is  a 
pre-established  harmony  between  the  movement  of  the 
monad  and  the  ideas  of  the  mind,  itself  a  monad. 
Mind  and  body  work  together  like  two  clocks,  set 
together  and  moving  at  the  same  rate. 

Much  controversy  arose  between  the  schools  of 
Locke  and  Leibnitz,  and  the  battle  raged  with  varying 
fortunes  until  Kant  threw  his  influence  on  the  side  of 
the  latter.  The  origin,  extent  and  limits  of  know- 
ledge were  examined  in  his  Critique  of  the  pure  reason, 
by  the  latter  meaning  reason  independent  of  experi- 
ence. He  established  the  twelve  categories  or  original 
conceptions  of  the  mind, — unity,  plurality,  totality, — 
reality,  negation,  limitation, — substantiality,  causality, 
reciprocal  action, — possibility,  necessity,  existence, — as 
253 


HERMANN  VON  HELMHOLTZ 

the  forms  by  which  judgments  are  conditioned.  He 
also  made  the  important  distinction  between  judgments 
a  posteriori  and  judgments  a  priori.  A  judgment 
a  posteriori  is  founded  on  experience.  On  the  other 
hand,  a  judgment  a  priori  is  one  having  the  marks  of 
universality  and  necessity.  Thus  the  latter  judgments 
are  either  absolutely  independent  of  experience,  or  they 
are  relatively  independent,  in  the  sense  that  the  con- 
ceptions employed  are  deduced  from  other  conceptions 
which  had  been  previously  derived  from  experience. 
He  assumes  that  the  necessity  and  universality  of  a 
priori  judgments  cannot  arise  from  any  combination  of 
experiences.  Again,  he  draws  a  distinction  between 
analytical  and  synthetical  judgments.  If  by  analys- 
ing the  conception  of  the  subject  we  find  the  predicate, 
or  if  the  subject  and  the  predicate  are  identical,  the 
judgment  is  analytical ;  but  if  the  conception  of  the 
subject  does  not  contain  the  predicate,  so  that  the 
latter  must  be  added  to  it,  the  judgment  is  synthetical. 
Synthetic  judgments  fall  into  two  classes :  those 
synthetic  a  posteriori^  in  which  the  synthesis  of  subject 
and  predicate  is  effected  by  experience  ;  and  those 
synthetic  a  priori^  if  the  synthesis  occurs  apart  from  all 
experience.  Some  a  priori  judgments  are  thus 
synthetic,  such  as  those  of  mathematics.  The  funda- 
mental judgments  of  arithmetic,  such  as  6  =  6,  are 
analytic,  but  all  those  of  geometry,  such  as  the  so- 
called  axioms  of  Euclid,  have  the  marks  of  strict 
universality  and  necessity,  and  are  synthetic  a  priori. 
254 


HIS  PHILOSOPHICAL  POSITION 

He  places  in  the  same  group  even  general  physical 
conceptions,  such  as  the  indestructibility  of  matter. 
Such  statements,  according  to  Kant,  are  true  apart 
from  all  experience.  In  like  manner  the  law  of 
causality,  our  conceptions  of  time  and  space,  our  con- 
ceptions of  space  in  three  dimensions,  are  of  tran- 
scendental origin,  we  possess  them  a  priori^  they  are 
born  in  us,  or,  to  use  the  technical  word,  they  are 
nativistic. 

Helmholtz  was  early  brought  into  collision  with 
this  aspect  of  Kant's  philosophy.  It  seemed  to  him  to 
imply  that  some  conceptions  came  from  without,  or, 
rather,  that  they  were  placed  in  the  mind  by  an 
external  or  supernatural  power,  an  implication  that 
conflicted  with  the  scientific  view  of  the  universe. 
In  the  tract  on  the  conservation  of  energy,  Helmholtz 
asserts  *  that  Science,  whose  object  is  to  understand 
nature,  must  start  from  the  assumption  of  its  intelligi- 
bility.' In  other  words,  nature  must  explain  herself, 
and  she  must  hold  all  the  contents  necessary  for  an 
explanation  of  everything.  His  subsequent  physio- 
logical studies,  more  especially  those  on  the  senses,  led 
him  to  different  notions  as  to  the  way,  for  example, 
in  which  an  animal  becomes  cognisant  of  the  outer 
world.  It  does  so  by  the  use  of  its  sense  organs  and 
by  the  movements  of  its  limbs.  The  latter  are  at  first 
apparently  purposeless,  but,  by  a  kind  of  education, 
they  are  brought  into  relation  with  sensory  impressions. 

He  appears,  however,  to  have  felt  the  force  of  the 
255 


HERMANN  VON  HELMHOLTZ 

objection  to  the  empiristic  view  of  things  that  some 
animals,  when  newly  ushered  into  the  world,  seem 
already  to  possess  a  large  amount  of  knowledge.  He 
remarks  :  *  The  accuracy  of  movement  of  many 
new-born  animals,  or  of  those  who  have  just  escaped 
from  the  egg,  is  very  striking  ;  the  less  mentally 
endowed  these  are,  the  sooner  do  they  learn  all  they 
can  possibly  learn.  The  newly-born  human  child, 
on  the  contrary,  is  very  slow  in  acquiring  visual 
perception ;  it  takes  several  days  to  learn  how  to 
judge  as  to  the  way  in  which  it  has  to  turn  its 
head  to  reach  the  mother's  breast.  Young  animals 
seem  to  be  more  independent  of  individual  experience. 
But  what  this  instinct  is  which  guides  them  may  be 
....  those  are  matters  of  which  as  yet  we  know 
practically  nothing  (dariiber  wissen  wir  Bestimmtes 
noch  so  gut  wi  nichts).'1 

This  matter,  however,  does  not  seem  so  inexpli- 
cable in  the  light  of  the  Darwinian  hypothesis,  with 
which  Helmholtz  often  expressed  his  general  agree- 
ment. If  the  origin  of  an  eye  or  an  ear  can  be  so 
far  explained  by  the  Lamarckian  principle  of  the 
adaptations  of  an  organ  to  its  environment,  and  if  this 
be  supplemented  by  the  law  of  variation  and  sur- 
vival of  the  fittest,  it  does  not  seem  difficult  to 
explain  the  gradual  accumulation  of  experiences 
through  countless  generations  leading  to  the  forma- 

1  Quoted  by  Du  Bois  Raymond.  Gedachtnissrede,  s.  39.  Berlin, 
1896. 

256 


HIS  PHILOSOPHICAL  POSITION 

tion  of  what  are  termed  instinctive  habits.  Thus 
we  may  account  for  the  origin  of  even  a  priori 
conceptions.  These  seem  to  be  so  universal,  so  true 
when  stated,  that  the  element  of  experience  in  their 
formation  is  overlooked.  In  this  way  the  mind  is 
not  a  clean  tablet,  as  supposed  by  Locke,  but  it  is 
a  tablet  already  modified  by  the  accumulated  experi- 
ences of  a  pedigree.  The  great  difficulty  met  with 
in  such  lines  of  thought,  is  the  question  of  why 
modifications  go  on  in  a  particular  line  and  appar- 
ently with  a  determinate  end  ?  Why  are  organs 
modified  in  a  particular  direction  ?  why  has  the 
physical  subtratum  of  mind  been  gradually  so 
built  up  that  certain  statements,  and  not  others,  are 
recognised  as  intuitive  ?  The  evolution  hypothesis, 
while  it  may  apparently  reconcile  the  empiristic  and 
nativistic  views  of  the  origin  of  certain  conceptions, 
as  held  by  Spencer  and  Du  Bois  Reymond,  does  not 
explain  the  whole  matter.  It  is  certainly  difficult, 
as  stated  by  Du  Bois  Reymond  himself,  to  reconcile 
with  the  empirical  theory  the  fact  that  a  butterfly 
only  just  escaped  from  the  larval  state  should,  during 
its  short  existence  as  it  flits  from  flower  to  flower, 
apparently  recognise  and  know,  as  if  from  experience, 
space  in  its  three  dimensions,  the  resistance  of  the  air, 
the  feeling  of  falling,  and  be  able  to  discriminate  the 
colours  of  flowers.  As  it  could  not  have  gathered 
experience  of  these  things  during  its  lowly  life  as  a 
caterpillar  on  a  cabbage  leaf,  in  what  stage  or  stages 
R 


HERMANN  VON  HELMHOLTZ 

of  its  ancestral  existence  did  it  acquire  this  experi- 
ence ?  We  may  be  able  to  answer  this  question 
when  we  have  full  knowledge  of  the  whole  evolution 
of  insect  life,  but  at  present  it  is  a  mystery.  It  is 
still  more  difficult  to  understand,  on  the  empiristic 
theory,  how  the  human  infant,  during  the  first  three 
months  of  its  life,  learns  to  use  its  hands  and  eyes 
for  a  definite  purpose.  Does  it  begin  to  acquire 
knowledge  by  a  series  of  more  or  less  successful  ex- 
periments, or  is  there  something  even  here,  acquired  by 
long  ancestral  experience,  that  tells  the  child  it  need 
not  try  to  grasp  the  moon,  while  it  makes  a  mistake 
with  the  gaslight  near  it  and  burns  its  little  fingers  ? 
Helmholtz  supported  the  empiristic  point  of  view 
by  questioning  the  correctness  of  Kant's  ideas  as  to 
the  nature  of  space,  and  the  a  priori  truth  of  the 
axioms  of  geometry.  As  early  as  1852,  while  in 
Konigsberg,  at  the  very  university  in  which  Kant 
lectured  for  many  years,  Helmholtz  published  an 
important  lecture  on  the  nature  of  human  sensa- 
tions.1 Then  he  critically  examined  such  questions, 
in  the  last  section  of  his  work  on  physiological  optics, 
laying  down  the  fundamental  proposition,  that  sensa- 
tions are  for  consciousness  only  signs,  the  interpretation 
of  which  is  given  by  the  intelligence.  For  vision, 
these  signs  give  intensity,  quality  (colour),  and,  in 
relation  to  the  part  of  the  retina  affected,  what  he 
terms  the  local  sign,  that  is  the  apparent  position. 

1  Whsenschaftl.  Abhandlungen,  Bd.  ii.,  9.  591. 
258 


HIS  PHILOSOPHICAL  POSITION 

Notions  of  extent  and  of  movement  are  not  derived 
necessarily  from  visual  perceptions,  but  from  the 
feeling  of  movement  due  to  muscular  contractions, 
and  even  to  the  degree  of  innervation  felt  to  be 
necessary  for  a  particular  movement.  Other  im- 
pressions are  added  to  those  of  the  visual  organs ; 
thus  the  eyes  or  head  are  moved  so  as  to  see  the  object 
in  different  positions ;  it  is  touched,  etc.,  and  the 
ensemble  of  all  possible  sensations  gives  rise  to  the 
representation  of  the  object  to  the  mind.  This  is 
perception,  when  applied  to  actual  sensations,  or  it 
may  be  a  representation  due  to  memory.  The 
psychical  act  is  the  association  of  the  signs  derived 
from  the  organs  of  sense,  or  the  association  of  re- 
presentations. 

In  1866,  two  elaborate  papers  appeared  on  the 
axioms  of  geometry  ;  a  synopsis  of  these  was  placed 
before  English  readers  in  1870  ; l  there  was  a  popular 
lecture  on  the  same  subject  in  1876;  in  the  same 
year,  and  in  1877,  two  papers  were  published  on 
the  origin  and  meaning  of  geometrical  axioms,2 
and  in  1894,  the  year  of  his  death,  a  last 
paper  on  the  accurate  explanation  of  sensory  im- 
pressions.3 

There  can  be  no  doubt  the  researches  of  Helm- 
holtz  into  the  phenomena  of  single  vision  with  two 

1  The  Academy )  vol.  i.,  p.  128. 

2  Mind,  vol.  i.,  p.  301  ;  also  vol.  iii.,  p.  212. 

3  Zeitsch.fur  PsycAologie  und  Physiologic  der  Sinnesorgane,  Bd.  7,  s.  18. 

259 


HERMANN  VON  HELMHOLTZ 

eyes,  the  theory  of  corresponding  points,  and  the 
mathematical  investigation  of  the  geometrical  form 
of  the  horopter  in  different  circumstances,  led 
Helmholtz  to  question  Kant's  doctrine  of  space. 
The  philosopher  of  Konigsberg  taught  that  space 
and  time  are  forms  of  intuition.  Space  is  the  form  of 
external  sensibility,  that  is  our  sense  of  the  relative 
positions  of  things  in  the  outer  world  ;  while  time 
is  in  the  form  of  internal  and  external  sensibility 
jointly,  that  is  our  sense  of  the  relative  sequences 
of  events.  On  the  a  priori  nature  of  space  depends 
the  validity  of  geometrical  judgments.  On  the  a 
priori  nature  of  time  arithmetical  judgments  depend. 
Things  in  themselves  related  neither  to  space  nor 
to  time  are  unknowable  to  man.  Co-existence  and 
succession  are  only  in  phenomena  and  are  only  in 
the  perceiving  subject.  Now  Helmholtz  found  in 
the  study  of  the  horopter,  that  two  different  sensa- 
tions arising  from  the  picture  on  each  retina  are 
blended  together  in  consciousness,  that  this  blending 
cannot  be  anatomically  explained,  and,  indeed,  has 
no  anatomical  foundation,  and  that  it  is  due  to  a 
mental  act,  which  is  the  result  of  experience.  We 
cannot  separate  the  part  due  to  the  immediate  sen- 
sation from  the  part  due  to  experience.  There  is 
not  a  perfect  agreement  between  the  external  object 
and  the  mental  representation,  except  in  a  mathe- 
matical sense.  The  feeling  of  localisation  in  space 
is  not  inborn,  but  is  the  result  of  an  act  of  reason 
260 


HIS  PHILOSOPHICAL  POSITION 

or  intelligence.  It  is  not  necessary  to  establish  a 
harmony  between  local  visual  signs  and  certain  corre- 
sponding positions  in  space,  but  there  is  a  harmony 
between  the  laws  of  representation  and  of  thinking 
and  those  of  the  outer  world. 

Among  the  elementary  propositions  of  geometry 
there  are  some  that  are  held  not  to  require  proof. 
There  are  the  axioms,  such  as,  (i)  if  the  shortest 
line  drawn  between  two  points  is  called  straight, 
there  can  be  only  one  straight  line  ;  (2)  through 
any  three  points  in  space,  not  lying  in  a  straight 
line,  a  plane  may  be  drawn,  that  is,  a  surface  which 
will  include  every  straight  line  joining  any  two  of 
its  points  ;  and  (3)  through  a  point  lying  without 
a  straight  line  only  one  straight  line  can  be  drawn 
parallel  to  the  first  ;  so  that  two  straight  lines  that 
lie  in  the  same  plane  and  never  meet,  however  far 
they  may  be  produced,  are  called  parallel.  Again 
there  are  such  propositions  as  that  a  solid  is  bounded 
by  a  surface,  a  surface  by  a  line,  and  a  line  by  a 
point ;  that  the  point  is  indivisible,  that  by  the 
movement  of  a  point  a  line  is  described,  by  that  of 
a  line  a  line  or  a  surface,  by  that  of  a  surface  a 
surface  or  a  solid,  and  by  the  movement  of  a  solid 
a  solid  and  nothing  else  is  described.1  The  question 
arises,  how  far  results  of  experience  have  become  mixed 
up  with  logical  processes  ?  Now,  in  problems  of  geo- 
metrical construction,  these  axioms  are  true  in  all 

1  Mind,  vol.  i.,  p.  302. 
26l 


HERMANN  VON  HELMHOLTZ 

conceivable  circumstances.  The  Euclidean  method 
of  proof  is  to  establish  the  congruence  of  lines, 
angles,  plane  figures,  solids,  etc.,  and  this  is  done 
by  applying  the  one  figure  to  the  other,  without 
changing  their  form  or  dimensions.  But  the  method 
of  establishing  congruence  implies  mechanical  move- 
ments, and  by  mechanical  movements  we  acquire 
experience.  If  so,  every  proof  of  congruence  rests 
upon  experience. 

To  illustrate  this  point  of  view,  Helmholtz  imagines 
beings  with  perceptions  like  our  own  living  in  worlds 
differing  from  our  own.  The  mind  can  readily  con- 
ceive beings  of  two  dimensions  living  on  a  plane 
surface,  and  so  confined  to  it,  that  they  had  no 
power  of  perceiving  anything  outside  this  sur- 
face. The  geometry  of  such  beings  would  show 
that  the  movement  of  a  point  described  a  line;  and 
that  of  a  line  described  a  surface  j  but  they  could 
not  even  imagine  the  form  produced  by  the  surface 
moving  out  of  itself,  so  as  to  describe  say  a 
sphere  or  a  cone.  Living  on  an  infinite  plane, 
their  geometry  would  be  like  planimetry.  Again, 
we  can  conceive  of  intelligent  beings  living  not  on 
a  plane  but  on  the  surface  of  a  sphere.  Their 
shortest  line  would  then  be  an  arc  of  the  great 
circle  passing  through  its  ends.  On  a  plane  there 
could  be  only  one  shortest  line  between  any  two 
points,  and  in  general  this  is  also  true  of  two  points 
on  a  spherical  surface,  except  when  the  two  points 
262 


HIS  PHILOSOPHICAL  POSITION 

are  diametrically  opposite  one  another,  in  which  case 
an  infinite  number  of  shortest  lines  (t.e.t  great 
circles)  can  be  drawn  between  them.  Sphere- 
dwellers,  as  Helmholtz  calls  them,  would  know 
nothing  of  parallel  lines  ;  they  would  say  that  two 
'straight'  (portions  of  great  circles)  lines,  sufficiently 
produced,  must  cut  in  two  points,  or  form  parts  of  the 
same  'straight'  line.  The  sum  of  the  angles  of  a 
triangle  would  always  be  greater  than  two  right 
angles,  increasing  as  the  surface  of  the  triangle  became 
greater.  Helmholtz  also  imagined  the  geometry  of 
intelligent  beings  living  on  the  surface  of  an  egg- 
shaped  body,  or  rather  we  must  think  of  egg-shaped 
space.  They  would  find  it  impossible  to  construct 
two  congruent  triangles  at  different  parts  of  the 
surface.  A  triangle  constructed  near  the  pole  would 
not  be  congruent  with  one  at  the  equator.  The 
periphery  of  a  circle  described  at  the  blunt  end  of 
the  body  would  be  greater  than  that  at  the  narrower, 
although  the  radii  were  equal,  the  radii  being  always 
measured  by  shortest  lines  on  the  surface.  He  then 
discusses  the  geometry  of  what  is  called  a  pseudo- 
spherical  surface  (a  curious  surface,  of  which  a  strip 
may  be  represented  by  the  inner  surface — turned 
towards  the  axis — of  a  solid  arch  or  ring,  the  curves 
of  which  are  infinitely  continued  in  all  directions). 
Such  a  surface  was  first  investigated  by  Beltrami. 
The  straightest  lines  of  the  pseudo-sphere  may  be 
infinitely  produced,  but  they  do  not,  like  those 
263 


HERMANN  VON  HELMHOLTZ 

of  a  sphere,  return  on  themselves.  On  such  a 
surface,  also,  as  on  a  plane,  only  one  shortest  line 
is  possible  between  any  two  points,  but  the  axiom 
as  to  parallels  does  not  hold  good.  Like  the 
plane  and  the  sphere,  it  has  its  measure  of  curva- 
ture constant,  so  that  figures  constructed  on  one 
part  of  the  surface  can  be  transferred  to  any 
other  place  with  perfect  congruence  of  form  and 
perfect  equality  of  all  dimensions  lying  on  the 
surface. 

It  can  also  be  shown,  by  a  method  devised  by 
Riemann,  that  the  space  in  which  we  live  is  three- 
fold, a  surface  is  two-fold,  and  a  line  is  an  aggregate 
of  points.  Time  is  also  an  aggregate  of  one  dimen- 
sion. Colour  is  an  aggregate  of  three  dimensions, 
because  each  colour  may  be  represented  by  a  mixture 
of  three  primary  colours,  taken  in  definite  proportions, 
as  may  be  shown  by  Clerk  Maxwell's  colour  top. 
But  Helmholtz  goes  still  further.  He  shows  that  we 
can  depict  the  appearance  of  a  spheric  or  of  a  pseudo- 
spheric  world,  or  such  a  world  as  we  see  in  a  con- 
vex mirror.  Suppose  we  looked  at  things  through 
specially-constructed  convex  glasses,  we  would  at 
first  be  confused,  more  especially  by  illusions  of  com- 
parative size  and  distance,  but,  by  experience,  the 
space  would  cease  to  be  strange.  It  is  clear,  there- 
fore, according  to  this  argument,  that  the  axioms  of 
geometry  do  not  all  hold  good  in  different  varieties 
of  space.  Taken  by  themselves  out  of  all  connection 
264 


HIS  PHILOSOPHICAL  POSITION 

with  mechanical  propositions,  they  represent  no  rela- 
tions of  real  things.  '  When  thus  isolated,  if  we  regard 
them  with  Kant  as  forms  of  intuition  transcendentally 
given,  they  constitute  a  form  into  which  any  empiri- 
cal content  whatever  will  fit,  and  which  therefore 
does  not  in  any  way  limit  or  determine  beforehand 
the  nature  of  the  content.  This  is  true,  however, 
not  only  of  Euclid's  axioms,  but  also  of  the  axioms 
of  spherical  and  pseudo-spherical  geometry.  As  soon 
as  certain  principles  of  mechanics  are  conjoined 
with  the  axioms  of  geometry,  we  find  a  system  of 
propositions  which  has  real  import,  and  which  can 
be  verified  or  overturned  by  empirical  observation, 
or  from  experience  it  can  be  inferred.  If  such  a 
system  were  to  be  taken  as  a  transcendental  form 
of  intuition  and  thought,  there  must  be  assumed 
a  pre-established  harmony  between  form  and 
reality.' J 

In  our  space  of  three  dimensions,  we  can  give  up, 
as  it  were,  what  we  possess,  and  be  able  to  imagine 
a  space  of  two  dimensions  inhabited  by  creatures 
having  no  thickness,  and  living  between  two  layers 
infinitely  close  together,  so  that  they  could  move 
from  side  to  side  and  backwards  and  forwards  ;  or 
a  space  of  one  dimension,  like  a  tunnel,  in  which 
creatures  having  no  thickness  and  no  breadth  could 
move  only  backwards  and  forwards.  We  cannot, 
however,  go  the  other  way  and  conceive  a  space  of 

1  Mind,  vol.  i.,  p.  321. 
265 


HERMANN  VON  HELMHOLTZ 

four  dimensions,  because  we  have  no  organs  by  which 
such  a  conception  can  be  formed  ;  but  it  does  not 
follow  that  there  may  not  exist  space  of  four  dimen- 
sions, or,  indeed,  of  any  number  of  dimensions.  If 
anything  we  saw  slipped  into  the  fourth  dimensional 
space  it  would  vanish  from  our  eyes,  and  we 
would  be  quite  unable  either  to  follow  it  or  to 
imagine  whither  it  had  gone.  The  point,  however, 
is,  that  intelligent  creatures  living  in  a  two-dimen- 
sional or  in  a  one-dimensional  space  could  develop 
a  geometry  of  their  own,  in  which  the  axioms  would 
be  like  our  own  Euclidean  axioms.  Further,  such 
intelligent  beings  living  on  a  spherical  or  a  pseudo- 
spherical  surface,  in  which  Euclidean  axioms  do  not 
hold  good,  might  develop  a  spherical  or  a  pseudo- 
spherical  geometry.  Such  non-Euclidean  geometries 
have  actually  been  worked  out  in  some  detail  by 
Lobatschewsky  of  Kasan,  and  Beltrami  of  Bologna. 
Helmholtz,  from  these  mathematical  speculations, 
concludes  :  (i)  that  Kant's  assumption  of  the  a  priori 
nature  of  the  axioms  is  not  proved  ;  (2)  that  it  is 
unnecessary  ;  and  (3)  that  it  is  useless  for  the  explana- 
tion of  the  real  world.  Still  he  takes  care  not  to 
deny  that  space  may  be  transcendental,  even  although 
the  axioms  of  geometry  may  not  be  so,  but  are 
ultimately  founded  on  our  experience  of  the  state  of 
things  in  the  space  in  which  we  live.  The  axioms 
then  are  empirical  and  are  derived,  like  other  laws  of 
nature,  from  observation  and  induction.  Helmholtz, 
266 


HIS  PHILOSOPHICAL  POSITION 

however,  admitted  that  the  law  of  causality  is  tran- 
scendental.1 

In  a  later  paper,  written  in  1888,  dedicated  to 
Eduard  Zeller  on  the  occasion  of  his  jubilee,  Helm- 
holtz  endeavoured  to  disprove  that  the  axioms  of 
arithmetic  were  also  a  priori  truths. 

1  For  a  criticism  of  Helmholtz's  papers  on  the  axioms  of  geometry, 
the  reader  is  referred  to  a  paper  by  W.  Stanley  Jevons  in  Nature,  vol.  iv., 
p.  481,  1871.  See  also  Helmholtz's  lecture  on  The  Origin  and  Significance 
of  Geometrical  Axioms.  Lectures,  2nd  series,  p.  27.  London,  1881. 


267 


CHAPTER    XVIII 

HELMHOLTZ     ON     ESTHETICS 


is  still  one  department  of  human 
-*-  thought  in  which  Helmholtz  made  his  mark. 
His  manifold  studies  in  the  physiology  of  vision  and 
of  hearing  brought  him  into  relationship  with  the 
principles  of  art,  and  with  that  branch  of  philosophy 
which  we  include  under  the  name  of  aesthetics.  He 
was  a  lover  of  art  in  all  its  forms,  and  the  contempla- 
tion of  works  of  art  was  one  of  his  favourite  recrea- 
tions. The  writings  of  Kant,  Schelling,  Hegel,  and 
Schopenhauer  on  art  were  familiar  to  him,  and 
although  he  did  not  agree  with  the  metaphysical 
conceptions  on  which  many  of  their  notions  were 
founded,  his  writings  show  that  they  exercised  an 
important  influence  on  his  ideas.  On  the  whole,  his 
notions  as  to  what  constitutes  the  beautiful  lean  to 
those  of  Kant,  namely,  that  the  beautiful,  through 
the  harmony  of  its  form  with  the  faculty  of  know- 
ledge, awakens  a  disinterested,  universal,  and  necessary 
satisfaction.  Art  is  not  merely  the  pleasure  of  the 
senses  ;  it  has  in  view  the  feeling  of  pleasure,  but  it 
always  implies  judgment.  It  must  be  free  from 
268 


HELMHOLTZ  ON  ESTHETICS 

the   restraint  of  arbitrary  rules,  as  if  it   came   from 
nature. 

'  No  doubt,'  he  says  in  summing  up  the  results  of 
the  volume  on  Sensations  of  Tone, c  is  now  entertained 
that  beauty  is  subject  to  laws  and  rules  dependent  on 
the  nature  of  human  intelligence.  The  difficulty 
consists  in  the  fact  that  these  laws  and  rules,  on 
whose  fulfilment  beauty  depends,  and  by  which  it 
must  be  judged,  are  not  consciously  present  to  the 
mind,  either  of  the  artist  who  creates  the  work,  or 
the  observer  who  contemplates  it.  Art  works  with 
design,  but  the  work  of  art  ought  to  have  the  appear- 
ance of  being  undesigned,  and  must  be  judged  on 
that  ground.  Art  creates  as  imagination  pictures, 
regularly  without  conscious  law,  -designedly  without 
conscious  aim.  A  work,  known  and  acknowledged 
as  the  product  of  mere  intelligence,  will  never  be 
accepted  as  a  work  of  art,  however  perfect  be  its 
adaptation  to  its  end.  .  .  .  And  yet  we  require 
every  work  of  art  to  be  reasonable,  and  we  show 
this  by  subjecting  it  to  a  critical  examination.  .  .  . 
The  more  we  succeed  in  revealing  the  harmony  and 
beauty  of  all  its  parts,  the  richer  we  find  it,  and  we 
even  regard  it  as  the  principal  characteristic  of  a  great 
work  of  art  that  deeper  thought,  reiterated  observa- 
tion, and  continued  reflection  show  us  more  and 
more  clearly  the  reasonableness  of  all  its  individual 
parts.' I 

1  Sensations  of  Tone,  p.  569. 
269 


HERMANN  VON  HELMHOLTZ 

Helmholtz  also  recognised  the  ethical  importance 
of  art,  or  rather,  as  expressed  by  Herbart,  that  ethics 
constituted  a,  perhaps  the  most,  important  part  of 
aesthetics.  Kant  also  held  that  the  beautiful  claims 
the  assent  of  all  as  a  symbol  of  the  morally  good. 
Helmholtz  writes,  *  Remembering  the  poet's  words — 

Du  gleichst  dem  Geist,  den  du  begreifst,1 

we  see  that  those  intellectual  powers  which  were  at 
work  in  the  artist  are  far  above  our  conscious  mental 
action,  and  that,  were  it  even  possible  at  all,  infinite 
time,  meditation,  and  labour  would  have  been  necessary 
to  attain  by  conscious  thought  that  degree  of  order, 
connection,  and  equilibrium  of  all  parts  and  all 
internal  relations,  which  the  artist  has  accomplished 
under  the  sole  guidance  of  tact  and  taste,  and  which 
we  have  in  turn  to  appreciate  and  comprehend  by  our 
own  tact  and  taste,  long  before  we  begin  a  critical 
analysis  of  the  work.  It  is  clear  that  all  high 
appreciation  of  the  artist  and  his  work  reposes 
essentially  on  this  feeling.  In  the  first  we  honour 
a  genius,  a  spark  of  divine  creative  fire,  which  far 
transcends  the  limits  of  our  intelligent  and  conscious 
forecast.  .  .  .  Herein  is  manifestly  the  cause  of  that 
moral  elevation  and  feeling  of  ecstatic  satisfaction 
which  is  called  forth  by  thorough  absorption  in 
genuine  and  lofty  works  of  art.  We  learn  from  them 

1  Thou  art  like  the  spirit  thou  conceivest. 

270 


HELMHOLTZ  ON  AESTHETICS 

to  feel  that  even  in  the  obscure  depths  of  a  healthy 
and  harmoniously-developed  human  mind,  which  are 
at  least  for  the  present  inaccessible  to  analysis  by  con- 
scious thought,  there  slumbers  a  germ  of  order  that 
is  capable  of  rich  intellectual  cultivation,  and  we 
learn  to  recognise  and  admire  in  the  work  of  art, 
though  executed  in  unimportant  material,  the  picture 
of  a  similar  arrangement  of  the  universe,  governed 
by  law  and  reason  in  all  its  parts.  The  contempla- 
tion of  a  real  work  of  art  awakens  our  confidence 
in  the  originally  healthy  nature  of  the  human 
mind  when  uncribbed,  unharassed,  unobscured  and 
unfalsified.' I 

In  a  series  of  lectures  delivered  in  Cologne,  Berlin, 
and  Bonn,  and  summarised  in  a  paper  on  the  relation 
of  optics  to  painting,2  he  demonstrates  the  limitations 
imposed  on  truth  to  nature  in  artistic  representations. 
He  shows  how  the  painter  finding  that  binocular 
vision  shows  the  flatness  of  a  picture,  carefully  selects, 
partly  the  perspective  arrangement  of  his  subject,  its 
position,  and  its  aspect,  and  partly  the  lighting  and 
shading,  in  order  to  give  an  intelligible  image  of  its 
magnitude,  shape  and  distance.  He  illustrates  the 
condition  of  securing  a  truthful  representation  of 
aerial  light,  and  how  to  transform  the  scale  of 
luminous  intensity  so  as  to  secure  proper  shading  of 
colour.  He  then  writes,  *  The  artist  cannot  tran- 
scribe nature ;  he  must  translate  her  ;  yet  this 

1  Sensations  of  Tone,  p.  571.  a  Lectures,  p.  73.     London,  1881. 

27I 


HERMANN  VON  HELMHOLTZ 

translation  may  give  us  an  impression  in  the  highest 
degree  distinct  and  forcible,  not  merely  of  the  objects 
themselves,  but  even  of  the  greatly  altered  intensities 
of  light  under  which  we  view  them.  ...  If  in 
these  considerations,  my  having  continually  laid 
weight  on  the  lightest,  finest,  and  most  accurate 
sensuous  intelligibility  of  artistic  representation,  may 
seem  to  many  of  you  as  a  very  subordinate  point, — 
a  point  which,  if  mentioned  at  all  by  writers  on 
aesthetics,  is  treated  as  quite  accessory, — I  think  this 
is  unjustly  so.  The  sensuous  distinctness  is  by  no 
means  a  low  or  subordinate  element  in  the  action 
of  works  of  art  ;  its  importance  has  forced  itself  the 
more  strongly  upon  me  the  more  I  have  sought  to 
discover  the  physiological  elements  in  their  action.' 

This  brief  statement  contains  an  expression  of  the 
main  aesthetical  principles  enforced  by  Helmholtz. 
The  combination  of  qualities  found  in  him  was  of  the 
rarest  kind,  and  it  was  fitting  these  qualities  were 
brought  to  bear  on  such  questions.  Schelling  wrote 
that  science  in  its  highest  perfection  has  the  same 
problem  to  solve  as  art,  but  the  method  of  its 
solution  is  different.  In  science  the  method  may 
be  mechanical,  and  the  possession  of  genius  is  not 
absolutely  necessary,  but  genius  alone  can  solve 
artistic  problems.  In  Helmholtz  we  had  all  that 
science  could  teach,  and  all  that  genius  could 
inspire. 


272 


CHAPTER    XIX 

HELMHOLTZ    AS    A    LECTURER 

DURING  his  whole  life  Helmholtz  was  in  the 
habit  of  giving  occasional  lectures  of  a  popular 
character.  He  did  not  consider  that  it  was  a  waste 
of  his  time  or  beyond  his  province,  to  lay  before  an 
intelligent  audience  of  men  and  women  in  the  middle 
ranks  of  life,  the  results  of  his  own  scientific  enquiries. 
Lectures  of  this  description  were  not  common  in 
Germany,  and  in  this  matter  of  popular  exposition 
Helmholtz  was  one  of  the  first  to  attempt  the  ex- 
periment. In  a  preface  to  a  translation  into  German 
of  the  lectures  of  Tyndall,  Helmholtz  alludes  to  the 
fact  that  such  lectures  had  long  been  given  in 
England,  and  he  defends  the  practice  as  being  likely 
to  stimulate  thought  and  to  awaken  an  interest  in  the 
work  of  scientific  men.  There  can  be  no  doubt  that 
the  so-called  popular  lectures  of  Helmholtz  reach  the 
high-water  mark  in  this  class  of  literature.  Prepared 
with  great  care,  fitly  illustrated  by  experiment, 
delivered  with  dignity,  they  made  a  great  impression 
in  Germany,  and  indeed  all  over  the  world.  The 
s 


HERMANN  VON  HELMHOLTZ 

fame  of  Helmholtz  has  been  extended  by  these  lectures, 
which  have  brought  instruction  to  the  learned  and  the 
unlearned  alike.  In  the  printed  form,  and  even  in  the 
translations,  they  are  literary  productions  of  great 
completeness.  They  give  one  a  feeling  of  thorough- 
ness in  the  treatment  of  the  subject.  The  matter  is 
discussed  by  a  master,  who  brings  to  bear  upon  it  all 
his  wealth  of  learning  and  research,  while  there  is  the 
ever-enduring  interest  that  attaches  to  an  exposition 
by  one  who  is  giving  forth  from  his  own  treasury. 
The  lectures  of  Helmholtz  are  the  fruit  of  his  own 
thought  and  labour.  They  do  not  amuse ;  they 
instruct,  and  they  inspire.  They  are  usually  on 
difficult  subjects,  and  they  take  a  wide  and  com- 
prehensive survey.  In  the  popular  exposition  of  the 
phenomena  of  vision,  of  hearing,  of  the  qualities  of 
musical  tone,  of  colour  and  the  art  of  painting,  Helm- 
holtz stands,  in  his  own  field,  head  and  shoulders  above 
all  his  contemporaries. 

The  lecture  on  Goethe,  delivered  in  1853,  's 
specially  worthy  of  notice.1  It  was  supplemented 
by  a  paper  dealing  with  some  aspects  of  the  same 
subject,  read  in  1892  to  the  Generalversammlung  der 
Goethe-Gesellschaft  at  Weimar.  In  this  lecture  he 
describes  and  explains  the  great  poet's  researches  on 
colour,  and  shows  the  mental  bias  that  completely 
led  him  astray  in  his  theory  of  colour.  At  the 
same  time  he  extols  Goethe's  scientific  insight  as 

1  Lectures,  p.  33.     London,  1873. 
274 


HELMHOLTZ  AS  A  LECTURER 

shown  in  his  speculations  on  the  morphology  of  the 
skull  and  of  the  flower.  Other  great  lectures  are  on 
sensory  perceptions,  on  the  eye  and  vision,  on  the 
relation  of  the  natural  sciences  to  knowledge,  and  on 
geometrical  axioms. 

Worthy  of  notice  also  are  his  speech  in  memory 
of  his  great  teacher  Magnus,  and  a  rectorial  address 
on  the  academic  freedom  of  the  German  universities. 
In  the  latter  lecture  there  are  several  admirable 
examples  of  his  way  of  thinking  that  are  well  worth 
quotation  : — 

I.  German  Student  Life. — 'The  German  student 
is  the  only  one  who  tastes  an  unmingled  joy  at  the 
time  when,  in  the  first  delight  of  his  young  independ- 
ence, yet  free  from  the  anxieties  of  mercenary  work, 
he  may  consecrate  his  hours  exclusively  to  all  that  is 
noblest  and  best  in  science  and  in  the  conceptions 
of  humanity.  United  by  a  friendly  rivalry  with 
numerous  comrades  devoted  to  the  same  efforts,  he 
finds  himself  daily  in  intellectual  communication  with 
masters  from  whom  he  learns  what  is  the  movement 
of  thought  among  independent  spirits.  I  appreciate 
at  its  full  value  this  last  advantage,  when,  looking 
back,  I  recall  my  student  days  and  the  impression 
made  upon  us  by  a  man  like  Johannes  Miiller,  the 
physiologist.  When  one  feels  himself  in  contact  with 
a  man  of  the  first  order,  the  entire  scale  of  his  intel- 
lectual conception  is  modified  for  life ;  contact  with 
275 


HERMANN  VON  HELMHOLTZ 

such  a  man   is  perhaps    the   most    interesting    thing 
which  life  may  have  to  offer.' 

2.  Freedom. — '  There  is  here  for  feeble  characters  a 
gift  as  calamitous  as  it  is  precious  for  the  strong.  .  .  . 
But  the  state  and  the  nation  have  more  to  expect  from 
those  who  are  capable  of  supporting  liberty,  and  whose 
efforts  and  work  are  the  results  of  their  own  individual 
energy,  of  their  dominion  over  themselves,  and  their 
love  of  science.' 

3.  Professorial  Fitness. — c  The  doing  something  for 
the  progress  of  science  is  the  best  mark  of  a  man's 
fitness  to  educate.' 

4.  Use  of  Lectures. — c  A   good   exposition   demands 
from  the  listener  much  less  sustained  effort  than  a  bad 
one  ;  it  enables  the  subject  to  be  comprehended  much 
more  surely  and  much  more  completely,  and  with  a 
well-ordered  arrangement,  bringing  into  strong  relief 
the  principal  points  and  the  divisions,  much  more  can 
be  overtaken  in  the  same  space  of  time.' 

5.  Teachers. — *  He     who     wishes     to     inspire     his 
audience  with  a  complete  conviction  of  the  truth  of 
what  he  advances,  ought,  above  all,  to  know   from 
personal  experience  what  produces  conviction.     It  is 
necessary,  then,  that  he  should  have  known  how  to 
advance  alone  into  a  region  where  no  one  has  ever 
broken  ground  ;  in  other  words,  he  must  have  worked 
upon  the  frontiers  of  human  science  and  conquered  for 
himself  new  domains.     A  master  who  presents  only 
results  acquired  by  others,  suffices  for  scholars  to  whom 

276 


HELMHOLTZ  AS  A  LECTURER 

authority  is  given  as  the  source  of  their  science,  but 
not  for  those  who  desire  to  deepen  their  convictions 
to  their  final  foundations.' 

6.  Judgment  of  Students. — '  All  this  system  rests 
upon  the  idea  that  the  general  current  of  the  opinion 
of  the  students  cannot  long  be  at  fault.  The  majority 
among  them  come  to  us  with  a  reason  sufficiently 
formed  by  logic,  with  a  sufficient  habit  of  intellectual 
effort,  with  a  judgment  so  considerably  developed  by  a 
knowledge  of  the  best  models,  as  to  be  able  to  discern 
the  truth  from  a  phraseology  which  has  only  the 
appearance  of  truth.' 

One  of  the  greatest  lectures  given  by  Helmholtz 
is  on  Thought  in  Medicine,  delivered  on  2nd  August 
1877,  on  the  Anniversary  of  the  Foundation  of  the 
Institute  for  the  Education  of  Army  Surgeons.1  It 
opens  with  the  following  sentence :  '  It  is  now 
thirty-five  years  since,  on  the  2nd  of  August,  I  stood 
on  the  rostrum  in  the  hall  of  this  institute,  before  such 
another  audience  as  this,  and  read  a  paper  on  the 
operation  for  Venous  Tumours.  I  was  then  a  pupil 
of  this  institution,  and  was  just  at  the  end  of  my 
studies.'  When  he  delivered  the  lecture  on  Thought 
in  Medicine  he  was  Professor  of  Mathematical  Physics 
in  the  University  of  Berlin,  and  the  foremost  man 
of  science  in  Germany.  He  adds  :  c  I  rejoice,  there- 
fore, that  I  can  once  more  address  an  assembly, 

1  Lectures,  p.  199.      1881. 


HERMANN  VON  HELMHOLTZ 

consisting  almost  exclusively  of  medical  men  who 
have  gone  through  the  same  school.  Medicine  was 
once  the  intellectual  home  in  which  I  grew  up ; 
and  even  the  emigrant  best  understands  and  is  best 
understood  by  his  native  land.' 

It  would  be  well  if  every  young  medical  graduate 
throughout  the  world  were  presented  with  a  copy  of 
this  lecture  on  the  day  of  his  graduation. 


278 


CHAPTER    XX 

HELMHOLTZ    IN    BERLIN — CLOSING    YEARS   AND 
PERSONAL    CHARACTERISTICS 

T  T  ELMHOLTZ  devoted  much  time  and  atten- 
J-  A  tion  to  the  affairs  of  the  Technical  Institute 
during  the  last  few  years  of  his  life.  He  was  much 
esteemed  and  revered  by  the  staff,  whose  reward  was, 
as  one  of  them  said,  a  kind  glance,  or  a  pressure  of 
the  hand,  or  a  word  of  appreciation  from  the  master. 
His  great  mental  gifts,  his  splendid  record  of  work 
accomplished,  and  a  certain  nobility  of  nature  impos- 
sible to  describe,  combined  with  a  quiet,  unobtrusive 
manner,  brought  tokens  of  regard  for  Helmholtz  as 
the  years  passed  onwards.  The  Emperor  William  I. 
often  received  Helmholtz  in  the  domestic  circle  to 
discuss  with  him  some  of  the  more  recent  advances  in 
science,  and  he  was  also  in  close  intimacy  with  the 
Crown  Prince  Frederick  (afterwards  Emperor)  and 
his  Princess,  both  of  whom  took  the  deepest  interest  in 
everything  relating  to  Art  and  Science.  The  Emperor 
William  I.  ennobled  him,  and  in  doing  so  conferred 
distinction  not  only  on  Helmholtz,  but  on  the  ranks  of 
the  peerage.  Honours  of  many  kinds  flowed  in  upon 
279 


HERMANN  VON  HELMHOLTZ 

him  from  all  parts  of  the  world.  The  celebration  of 
his  seventieth  birthday  became  a  national  event,  and  a 
tribute  was  then  paid  to  his  eminence  as  a  man  of 
science  and  as  an  inspiring  teacher,  only  equalled  a  few 
years  ago  by  the  ceremonies  at  the  jubilee  of  his  friend 
Lord  Kelvin.  The  Emperor  William  II.  sent  him  an 
autograph  letter  in  ackowledgment  of  his  great  services 
to  science,  and  conferred  special  honours  upon  him. 
The  Kings  of  Sweden  and  Italy,  the  Grand  Duke  of 
Baden,  and  the  President  of  the  French  Republic, 
sent  him  the  insignia  of  various  orders.  Representa- 
tives of  academies,  universities,  and  learned  societies, 
sent  representatives  and  addresses.  A  Helmholtz  gold 
medal  was  struck  in  his  honour,  to  be  awarded  from 
time  to  time  for  distinguished  services  to  science,  and 
was,  at  a  banquet,  handed  to  Helmholtz  himself  as  its 
first  recipient,  after  a  brilliant  speech  by  his  life-long 
friend  Du  Bois  Reymond.  At  the  same  time  a  marble 
bust  by  Hildebrand  was  unveiled.1 

At  this  banquet  von  Helmholtz  delivered  a  speech, 
in  which  he  uplifted  the  veil  of  his  inner  life  and 
revealed  some  of  the  secret  influences  that  contributed 
to  his  marvellous  creativeness.  His  own  words,  in 
free  translation,  are  better  than  any  other.  Referring 
to  the  medal,  he  said, — 

*  It  is  the  greatest  honour  men  of  science  could  pay 

1  On  the  6th  of  June  1899,  a  marble  statue  of  von  Helmholtz  was 
unveiled  by   the   Emperor   William   II.,   in   front  of  the   University  of 
Berlin.     It  has   been    fittingly   placed   near  those   of   the   brothers   von 
Humboldt.     See  Daheim,  24th  June  1899,  No.  39,  p.  i. 
280 


HELMHOLTZ  IN  BERLIN 

to  me  to  connect  my  name  with  this  medal,  which 
will  stamp  the  progress  of  science  in  future  times. 
Science,  to  modern  humanity,  proclaims  peace.  The 
scientific  man  does  not  work  for  his  own  welfare,  but 
for  that  of  his  nation,  and  for  the  whole  of  humanity, 
especially  for  those  who  are  sufficiently  educated  to 
enjoy  the  fruits  of  science.  You  desire  to  associate 
my  name  with  this  medal,  and  to  hold  me  up  to 
coming  generations  as  an  example  of  an  investigator. 
I  waver  between  a  feeling  of  joy  and  a  feeling  of  grave 
responsibility.  I  have  a  proud  joy  that  the  result  of 
my  thoughts  is  to  work  on  to  future  generations  far 
beyond  my  individual  life.  You  will  also  understand 
that  as  a  father  cares  for  his  offspring,  and  endeavours 
to  help  them,  so  I  have  also  a  love  for  the  children  of 
my  thoughts.  These  contain  the  best  of  my  convic- 
tions ;  I  lay  upon  them  the  utmost  stress ;  and  I 
rejoice  if  the  further  development  of  science  is  to  be 
in  their  direction.  But  the  doubt  may  arise,  whether 
my  own  ideals  are  not  too  narrow,  and  my  principles 
sometimes  too  imperfect,  for  the  wants  of  humanity 
in  all  time.  If  so,  I  hope  the  awarders  of  this  medal 
in  the  future  will  not  confine  themselves  to  what  I 
have  accomplished ;  but  I  should  like  to  wave  on 
high  the  one  banner  on  which  are  inscribed  the 
words,  that  the  purpose  of  science  is  to  comprehend 
reality  and  the  play  of  phenomena  as  regulated  by 
law.' 

On  the  occasion  of  his  seventieth  birthday,  his  eye 
281 


HERMANN  VON  HELMHOLTZ 

was  undimmed  and  his  natural  force  was  unabated, 
and  it  was  hoped  that  he  had  yet  many  years  before 
him  to  complete  his  life  work  by  the  publication  of 
his  lectures.  He  attended  the  meeting  of  the  British 
Association  for  the  Advancement  of  Science,  in  Edin- 
burgh, in  1892,  and  while  years  were  evidently 
gathering  upon  him,  his  noble  appearance  made  a 
deep  impression  on  all  who  saw  him.  In  1893  ne 
visited  the  International  Exhibition  in  Chicago,  and 
afterwards  saw  something  of  the  grand  scenery  of 
North  America  and  Canada.  He  then  started  on 
the  homeward  journey.  Shortly  before  the  steamer 
reached  Hamburg  he  had  an  attack  of  giddiness,  and 
fell  down  the  stair  of  the  cabin.  The  injury  was 
severe,  causing  concussion  of  the  brain  and  great  loss 
of  blood  from  a  scalp  wound.  He  recovered  so  far, 
but  those  about  him  saw  strength  failing.  Now  easily 
tired,  work  became  more  and  more  difficult.  At  last 
the  brain  that  had  worked  so  well  gave  way,  and,  in 
July  1894,  he  had  a  stroke  of  apoplexy.  For  two 
months  he  lingered  on,  showing,  as  one  would  expect 
from  so  great  a  nature,  patience  and  calmness  in  look- 
ing forward  to  the  end.  This  came  on  the  8th  of 
September  1894,  when  he  had  lived  eight  days  beyond 
his  seventy-third  birthday.1 

1  In  the  ZeitscArift  fur  Ptychologle  of  March  /th,  Professor  David 
Hansemann,  of  Berlin,  published  a  report  of  his  examination  of  the 
brain  of  Helmholtz.  The  circumference  of  the  head  was  59  centi- 
metres, that  of  the  skull  55  centimetres.  The  breadth  of  the  skull 
was  I5'5,  and  its  length  18*3  centimetres.  The  cephalic  index  was 
282 


HELMHOLTZ  IN  BERLIN 

German  artists  have  preserved  for  all  time,  in 
marble  and  on  the  canvas,  Helmholtz's  personal 
appearance.  This  appearance  was  an  indication  of 
his  own  inner  strength.  Rather  above  the  middle 
stature,  he  had  a  firm,  erect  frame.  His  splendid 
head  was  well  thrown  back,  so  that  his  posture  was 
always  sure  to  command  attention.  The  shape  of 
the  head  was  perfect,  broad  between  the  eyes  but  not 
out  of  proportion.  The  eyes — 

*  Such  splendid  purpose  in  his  eyes  ' — 

were  full  of  intelligence,  not  so  brilliant  as  deep  and 
reflective.  They  often  had  that  far-away  look  so 
conspicuous  in  thinkers,  as  if  the  soul  were  away  on 
its  own  quest.  His  manner  was  dignified,  almost  to 
coldness,  but  it  was  at  the  same  time  courteous.  It 
is  said  that  he  had  occasionally  a  peculiar  look  that 
caused  a  shallow  man  to  stop  asking  questions  and  to 
feel  his  own  unworthiness.  With  those  who  were 
truly  in  earnest  he  would  take  infinite  pains  to  explain, 
listen  to  suggestions,  and  remove  difficulties.  Reserve 
was  his  habitual  attitude.  To  his  favourite  students, 
and  in  the  circle  of  his  own  friends,  there  was  always 

therefore  85-25,  showing  a  broad  head.  Helmholtz's  head  was  about 
equal  in  size  to  that  of  Bismarck,  and  rather  smaller  than  that  of  Wagner, 
both  of  whom  had  big  heads.  On  the  other  hand,  Darwin's  head  was 
only  56-3  centimetres  in  circumference.  The  weight  of  the  brain,  with 
its  blood,  was  1700  grams.,  without  the  blood,  1400  grams.,  being  about 
100  grams,  heavier  than  the  average  human  brain.  The  sulci  were  very 
deep  and  well  marked,  especially  in  those  parts  of  the  brain  which 
Flechsig  has  shown  to  be  concerned  in  associations.  The  frontal  con- 
volutions in  particular  were  deeply  cut  by  very  numerous  sulci. 
283 


HERMANN  VON  HELMHOLTZ 

the  charm  of  a  great  personality.  The  first  time  the 
writer  saw  him  was  in  1872,  in  the  Gewandhaus,  in 
Leipzig,  during  a  performance  of  Mendelssohn's  c  Mid- 
summer Night's  Dream.'  Near  the  orchestra  he  saw 
a  head  of  such  splendid  proportions,  with  the  eyes 
having  a  rapt  expression,  as  the  sensuous  music 
floated  through  the  hall,  and  he  thought  'that  must 
be  Helmholtz  ! '  It  could  be  no  other.  A  few  days 
later  he  saw  the  great  physicist  in  his  own  laboratory, 
and  received  kindly  advice  regarding  the  ophthal- 
mometer  and  acoustical  apparatus. 

Helmholtz  was  fond  of  mountaineering,  and  he  was 
an  excellent  swimmer.  Du  Bois  Reymond  says  that 
long  walks,  to  which  his  father  had  accustomed  him 
in  the  beautiful  surroundings  of  Potsdam,  had  more 
than  a  hygienic  value  for  him.  Helmholtz  himself 
tells  us  that  it  was  often  during  walking  that  the 
solution  of  problems  came  before  his  mind. 

Volkmann,  in  his  masterly  estimate  of  the  work  of 
Helmholtz,  remarks  that  one  of  his  chief  merits  was 
to  establish  a  harmony  between  the  vast  accumulation 
of  facts  that  characterised  the  period  comprehending 
the  middle  of  this  century  and  the  more  theoretical 
studies.  The  necessity  for  so  doing  was  early  felt  by 
Helmholtz  himself,  for  in  1874  we  find  him  saying, — 
c  It  seems  to  me  that  it  is  not  so  much  knowledge  of 
the  results  of  natural  science  which  the  wisest  and 
best  educated  men  seek,  as  an  aspect  of  the  mental 
activity  of  the  investigator,  a  view  of  his  scientific 
284 


HELMHOLTZ  IN  BERLIN 

system,  and  a  statement  of  the  goal  towards  which  he 
strives.  They  wish  to  know  what  his  work  has  done 
for  the  great  problems  of  human  life.' 

Helmholtz  indicates  his  position  in  the  words  he 
uses  regarding  his  pupil  Hertz.  '  He  takes  his  place 
among  those  who  see  the  advancement  of  humanity 
in  the  greatest  possible  development  of  their  spiritual 
talents  and  in  the  sovereignty  of  the  spirit  over  the 
natural  passions  and  the  hostile  powers  of  nature. 
To  bring  about  this  there  must  be  a  severe  mental 
discipline.  Thought,  the  will,  and  the  power  of 
action  must  be  brought  into  subjection.'  Helmholtz 
himself  submitted  to  a  life-long  discipline.  He  says  : 
— CI  have  never  considered  a  research  complete  until 
it  stood  before  me  perfect  and  without  logical  defects. 
It  was  always  formulated  in  writing.  My  conscience 
stood  before  my  mind  and  the  wisest  of  my  friends, 
and  I  asked  myself  if  they  approved  of  my  work. 
They  were  the  embodiment  of  the  scientific  spirit  of 
an  ideal  humanity  and  gave  me  my  measure. 

'  I  do  not  mean  to  say  that  in  the  first  half  of  my 
life,  when  I  had  still  to  work  for  my  outward  position, 
that  higher  ethical  motives  than  those  of  the  desire 
of  knowledge,  and  a  feeling  of  doing  my  duty  as  an 
officer  of  the  state,  influenced  my  life,  at  all  events  it 
was  not  easy  to  be  sure  of  their  existence  while 
egoistic  motives  compelled  me  to  work.  Most  in- 
vestigators feel  this.  But  later  on,  when  one's  posi- 
tion had  been  secured,  at  a  time  when  some  who, 
285 


r. 


HERMANN  VON  HELMHOLTZ 

having  no  inner  propelling  power  towards  science, 
cease  to  work,  a  higher  aspect  of  one's  relation  to 
humanity  came  into  the  foreground.  The  thoughts 
that  have  found  their  way  into  literature,  or  into  the 
minds  of  men  by  the  teaching  of  pupils,  continue  to 
have  an  independent  life  ;  these  thoughts  have  further 
developments,  and  inspire  teaching  on  newer  lines. 
One's  own  thoughts  are  of  course  more  in  one's 
spiritual  circle  of  vision  than  strange  ones,  and  one 
feels  satisfaction  when  he  sees  his  own  bearing  fruit. 
Then  a  paternal  feeling  springs  up  in  the  mind  of  the 
thinker,  and  he  cares  and  fights  for  the  advancement 
of  his  offspring.  Still,  the  whole  world  of  civilised 
humanity  is  before  him,  the  duration  of  whose  life 
seems  to  be  eternal  in  comparison  with  the  short  life 
of  an  individual.  The  investigator  then  sees  himself, 
with  his  small  contributions  to  the  building  up  of 
science,  in  the  service  of  an  eternal  sacred  cause,  to 
which  he  is  bound  by  the  closest  bonds  of  affection. 
By  this  thought  his  own  work  is  hallowed.  To  feel 
the  full  force  of  this,  one  must  have  had  the  experience.' 
Helmholtz,  in  a  speech  delivered  at  the  banquet,  tells 
us  something  of  his  mode  of  working.  When  a  problem 
came  before  his  mind  he  turned  it  round  on  all  sides. 
He  reflected  upon  it  for  several  days,  carefully  thinking 
out  the  details  of  any  experimental  procedures  that 
might  be  necessary.  In  the  solution  of  more  difficult 
questions,  the  light  seldom  came  when  he  was  at  his 
desk,  and  never  when  the  brain  was  fatigued.  It  was 
286 


HELMHOLTZ  IN  BERLIN 

usually  in  the  morning,  after  the  wearied  brain  had 
been  refreshed  by  sleep,  or  while  walking  up  a  hill- 
side, with  pure  air  and  bright  sunny  weather,  that  the 
truth  flashed  before  his  mental  vision.  Even  the 
smallest  amount  of  alcohol  he  found  interfered  with 
his  mental  work.  He  then  reduced  his  views  to  writ- 
ing, and  took  great  pains  in  giving  correct  expression 
to  what  he  wished  to  communicate.  In  literary  com- 
position he  was  extremely  fastidious,  often  writing  the 
manuscript  six  times  over,  and  next  day,  even  after 
this  severe  ordeal,  he  was  never  satisfied  with  what  he 
had  written. 

It  is  not  necessary  to  define  the  position  of  Helm- 
holtz  amongst  scientific  thinkers.  His  works  bear 
their  own  evidence.  There  is  a  general  consensus  of 
opinion  that  he  is  one  of  the  greatest  men  of  the 
present  century.  To  find  one  like  him  in  mental 
power  and  width  of  range,  we  must  go  back  to  such 
intellectual  giants  as  Descartes  and  Leibnitz,  and 
even  when  he  is  compared  with  them,  it  must  not  be 
forgotten  how  enormously  broader  was  the  field  of 
science  in  the  time  of  Helmholtz  than  in  the  seven- 
teenth century.  The  only  English  philosopher  with 
whom  he  may  be  compared  is  Thomas  Young. 
Both  were  remarkable  for  versatility  and  originality  ; 
both  had  the  same  wide  range  of  knowledge  ;  both 
were  manifold  men  of  science ;  both  were  physio- 
logists and  physicists ;  the  researches  of  both  were 
fundamental.  But  Helmholtz  was,  as  a  mathema- 
287 


HERMANN  VON  HELMHOLTZ 

tician  of  the  first  ranlc,  even  greater  than  Young.  It 
will  be  admitted  that,  taking  him  all  in  all,  Helmholtz 
is  the  greatest  Master  of  Medicine  the  world  has  ever 
seen. 

Of  Helmholtz's  opinions  on  religious  questions, 
nothing  can  be  stated  with  any  degree  of  precision. 
Such  topics  were  not  with  him  subjects  of  conversa- 
tion. But  throughout  his  writings  there  breathes  a 
spirit  of  reverence,  while  his  noble  and  pure  life  is 
the  highest  testimony  to  his  true  worth.  For  such  a 
man  a  time  surely  comes  when 

*  That  in  us  which  thinks  and  that  which  feels 
Shall  everlastingly  be  reconciled, 
And  that  which  questioneth  with  that  which  kneels.' 


288 


HERMANN  VON  HELMHOLTZ 

STRONG  soul,  whose  calm  and  almost  God-like  mien, 

Eyes  of  unfathomable  depth  of  thought, 

And  broad  and  lofty  intellectual  brow, 

Betoken  force  and  insight  :  Shall  I  try 

To  tread  the  path  you  followed  in  the  quest 

Of  Nature's  truth  ?     To  live  in  your  great  thoughts 

Is  like  to  breathing  a  pure  atmosphere 

On  lofty  mountain  peak,  in  azure  blue, 

While  all  around  are  pure  white  fields  of  snow, 

And  all  below  is  veiled  in  cloud  and  mist. 

And  when  I  find  atomic  mazy  dance, 

The  swift-winged  lightning,  colour's  sun-born  hues, 

The  tones  of  music  and  harmonious  chords, 

Fine  movements  and  the  throb  of  nervous  thrills 

That  course  so  swiftly  through  this  mortal  frame, 

The  hidden  work  of  wond'rous  ear  and  eye, 

Are  all  made  clear  and  plain  ;  then  comes  the  thought 

That  He  Who  made  all  these  did  also  send 

To  this  dull  earth  His  own  interpreter, 

A  great  and  gifted  intellect  like  thine, 

A  child  of  genius,  armed  at  every  point 

For  all  the  glorious  work  that  thou  hast  done, 

Revealing  Nature's  plans  ;  and  thou  hast  shown 

Man's  soul  is  tuned  to  Nature,  and  reflects 

All  things,  as  does  the  surface  of  a  lake 

Reflect  the  glories  of  the  earth  and  sky. 


BIBLIOGRAPHY 

1.  Hermann  von   Helmholtz.     Ein  Nachruf  von  Dr  J. 

Fernet,  Professor  der  Physik  am  Eidgenossischen 
Polytechnicum.  Neujahrsblatt  der  naturforsch- 
enden  Gesellschaft,  in  Zurich,  1895.  Ziirich, 
1894. 

2.  Hermann  von  Helmholtz.     Gedachtnissrede  gehalten 

in  der  Singakademie  zu  Berlin  am  14  Dezember 
1894,  von  Wilhelm  von  Bezold,  mit  einem 
Portrat  nach  einem  Olgemalde  von  Franz  von 
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Dr  E.  Landolt.  Archives  d'Ophtalmologie,  De"cem- 
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ten am  28  September  1894  in  der  Aula  der 
Universitat  Utrecht.  Von  Th.  W.  Engelmann. 
Leipzig,  1894. 

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du  Bois  Reymond.     Leipzig,  1897. 

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memoration of  his  yoth  Birthday,  by  Dr  Hugo 
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Dr  Arthur  Gamgee,  F.R.S.,  Emeritus  Professor  of 
Physiology  in  the  Owens  College,  Victoria  Uni- 
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Grundlagen  der  Mathematik  und  Mechanik. 
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nissfeier  am  7  Dezember  1894,  von  Dr  L.  Her- 
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Medicinalrath  z.  Z.,  President  der  Gesellschaft, 
und  Dr  P.  Volkmann,  ord.  Professor  der  Theor- 
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Professor  A.  W.  Riicker.  Proceedings  of  the  Royal 
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HERMANN  VON  HELMHOLTZ 

25.  Populare  Wissenschaftliche  Vortrage.     Braunschweig, 

1865-1876. 

26.  Handbuch     der     physiologischen     Optik.        Zweite 

ungearbeitete  Auflage.  Hamburg  und  Leipzig, 
1896. 

27.  Die     tylechanik     der     Gehorknochelchen     und    des 

Trommelfels.     Bonn,  1869. 

28.  Titelverzeichniss  sammtlicher  Veroffentlichungen  von 

Hermann  von  Helmholtz.     Leipzig,  1895. 

29.  Heinrich  Hertz.    Gesammelte  Werke.    3  Bande.    Mit 

einem  Vorwort  von  Hermann  von  Helmholtz. 
Leipzig,  1894-5. 

30.  Hertz.       Electric    Waves,    with    preface    by    Lord 

Kelvin.     London,  1893. 

31.  Vorlesungen  iiber    theoretische    Physik   von   H.  von 

Helmholtz,  herausgegeben  von  Arthur  Konig,  Otto 
Krigar-Menzel,  Franz  Richarz,  Carl  Runge.  Band 
i.-vi.  Leipzig. 


294 


INDEX 


ACCOMMODATION,  mechanism   of,    7, 

92,  94- 

Action,  at  a  distance,  203. 
Action,  definition  of  dynamical,  245. 
Action,  principle  of  least,  235,  240,  243. 
/Esthetics,  Helmhokz  on,  268. 
Aguilonius,  reference  to,  180. 
After  images,  177. 
Air,  micro-organisms  in,  29. 
Airy,  reference  to,  91,  118. 
Ampere,  210. 

Andrews,  Thomas,  reference  to,  91. 
Apparatus,  electrical,  for  physiology, 

36. 

Arm,  muscles  of,  Helmholtz  on,  170. 
Art,  ethical  importance  of,  270  ;  nature 

of,  269. 
Axioms  of  geometry,  Kant's  opinions 

as  to,  258. 

BABBAGE,    Charles,    use    of  silvered 

mirror  by,  77. 
Bach,  reference  to,  167. 
Bacon,  on  heat,  46. 
Baconian  philosophy  in  Germany,  12. 
Baden,  government  of,  184. 
Baden,  Grand  Duke  of,  reference  to, 

280. 
Balloons,  steering  of,  and  theory  of, 

203. 

Beats,  nature  of,  156,  158. 
Beethoven,  reference  to,  134. 
Behr,  reference  to,  77. 
Bell,  John  and  Charles,  reference  to, 

152. 

Beltrami,  reference  to,  266. 
Bentley,  reference  to,  203. 
Berlin,  Physical  Society  of,  24. 
Berlin,  University  of,  183,  239. 
Bernard,  Claude,  reference  to,  14. 
Bernoulli,  Daniel,  reference  to,  40. 
Bertrand,  reference  to,  195. 
Bessel,  reference  to,  70,  202. 
Bezold  W.  von,  reference  to,  218. 
Bibliography,  291. 
Binz,  reference  to,  182. 
Bismarck,  head  of,  283. 
Bones  of  the  ear,  133,  135. 


I  Bonn,  Helmholtz  on,  88. 
i  Bonn,  University  of,  129. 
'  Bowman,  physiologist,  reference  to,  14. 

Boyle,  Robert,  reference  to,  116. 

Branco,  Professor,  reference  to,  58. 

Brewster,  Sir  David,  reference  to,  91, 
112,  118,  119. 

British  Association,  Edinburgh  meet- 
ing 1892,  282. 

British  Association   meeting  at   Hull 
1854,  91. 

Brucke,  early  friendship  with   Helm- 
holtz, 10,  11,  13,  24,  25,  74,  77,  in. 

Brucke,  on  ciliary  muscle,  101. 

Butterfly,   life    of   a,   considered   em- 
pirically, 257. 

CAGNIARD  DE  LA  TOUR,  reference  to, 

26. 

Cape  d'Antibes,  192. 
Carnot,  Sadi,  reference  to,  50,  194. 
Carpenter,  reference  to,  14. 
Cayley,  Arthur,  reference  to,  190. 
Chicago,  International  Exhibition  at, 

282. 

Chladni,  plates  of,  20. 
Ciliary  muscle,  101,  102. 
Clang  tint,  143. 
Clapeyron,  on  heat,  50. 
Clausms,  physicist,  10,  23,  43,  194,  205. 
Clouds,  Helmholtz  on,  223. 
Coccius,  ophthalmoscope  of,  77. 
Cochlea,  action  of,  140,  141,  152. 
Coil, induction,  of  Du  BoisReymond,  36 
Colding,  on  energy,  50. 
Colour  blindness,  125. 
Colour,  Helmholtz's  researches  on,  112. 
Colour,  nature  of,  116. 
Combination  tones,  159,  161. 
Conservation  of  energy,  193,  242. 

Cooper,  Dr,  reference  to,  91. 
Copernicus,  reference  to,  19. 
Corresponding  retinal  points,  173,  178. 
Corti,  physiological  action  of  the  organ 

of,  151,  154. 
Coulomb,   reference    to,    21 ;    law    of 


electrical  attraction,  204. 


295 


INDEX 


Cramer,  on  accommodation,  95. 

Helmholtz  on,  211,  222  ;  on  specific 

Critique  of  pure  reason,  Kant's,  253. 
Gumming,  W.,  reference  to,  77. 

inductive  capacity,  205. 
Fechner,  reference  to,  13. 

Currents,  electrical,  effects  of  those  of 

Fermentation,   studies    by  Helmholtz 

short  duration,  in. 

on,  26. 

Cuvier,  reference  to,  21. 
Cyclic  systems,  Hemholtz  on,  234. 

Fingal's  Cave,  reference  to,  92. 
Fitness,  professorial,  Helmholtz  on,  276. 

Fluid,  nature  of,  195. 

D'ALEMBERT,  reference  to,  40,  52. 

Fluids,  discontinuity  in,  201. 

Darwin,  head  of,  283. 

Forbes,  on  ice,  221. 

Darwin,  reference  to,  19. 

France,  intellectual  life  in,  21. 

Darwinian  hypothesis  and  innate  ideas, 

Frederick    the     Great,   reference    to, 

256. 

236. 

Davy,  Humphry,  on  heat,  47. 
De  la  Tour,  Cagniard,  reference  to,  26. 

Frederick,  Crown  Prince,  reference  to, 
279. 

Democritus,  reference  to,  253. 

Freedom,  Helmholtz  on,  275. 

Descartes,   44,    46,    52,  96,   236,   252, 

French  Republic,  President  of,  refer- 

257. 

ence  to,  280. 

Difference  tones,  159. 

Fresnel,  reference  to,  114. 

Dispersion,  anomalous,  227. 

Frictionless  fluids,  196. 

Dissipation  of  energy,  193. 

Friedrich  Wilhelm  Institute,  reference 

Dissonance,  nature  of,  156. 

to,  40. 

Donders,  reference  to,  14,  82,  85,  97  ; 

Fourier's  theorem,  144,  167. 

reference  to  Cramer  by,  97  ;  on  vowel 

tones,  162  ;    on  movements  of  eye- 

GALILEO, reference  to,  19,  38,  242* 

balls,  177. 

Galvani,  reference  to,  31. 

Dove,  reference  to,  22,  43,  181. 

Gaugain,  galvanometer  of,  211. 

Draper,  reference  to,  118. 

Gauss,  reference  to,  221  ;  on  unit  of 

Drumhead,  action  of,  133,  135. 

force,  239. 

Du  Bois  Reymond,  reference  to,  n, 

Gay-Lussac,  reference  to,  27. 
Geometry,  axioms  of,  261, 

Ductus  cochlearis,  action  of,  152. 

Geometry,  non-Euclidean,  266. 

Dusch,  reference  to,  29. 

German  student  life,    Helmholtz  on, 

Dynamics,  Helmholtz  on  principles  of, 
233* 

Germany,  science  in,  during  early  part 

of  igth  century,  18. 

EAR,  bones  of,  133,  135. 

Goethe,  reference  to,  ri9,  221  ;  lecture 

Ear,  damping  arrangements  in,  150. 
Ear,  internal  description  of,  138. 

by  Helmholtz  on,  274. 
Goodsir,  John,  anatomist,  reference  to, 

Edinburgh,  reference  to,  92. 

14. 

Electric    interrupter,    of    Helmholtz, 

Graefe,  Von,  reference  to,  83. 

I6s-. 

Grassman,  reference  to,  205. 

Electricity,  animal,  66,  104. 

Grove,  W.  R.,  on  condition  of  physical 

Electricity,   theories    of,  203  ;    Helm- 

forces,  48,  91. 

holtz's  researches  in,  209. 
Electrodes,  non-polarizable,  105. 

Gruithuisen,  reference  to,  76. 

Electrodynamics,  203. 
Empirical  philosophy,  251. 

HALLER,  reference  to,  12  ;  on  rate  of 
nervous  impulse,  64. 

Encyclopaedists,  reference  to,  21. 

Hamilton,   William   Rowan,  91,   190, 

Energy,  conservation  of,  39,  193. 
England,  Helmholtz's  impressions  of, 

243  ;    principle  of   varying    action, 
235,  244. 

Erlach,  Von,  reference  to,  74. 

Hansemann,  David,  reference  to,  282. 
Harmonic  tones,  147,  148. 

Essex,  reference  to,  76. 

Hartley,  reference  to,  114. 

Ether,  theory  of  movements  in,  248. 

Hassenstein,   on  reflected   light  from 

Euclid,  anxioms  of,  254,  262. 

eye,  74. 

Euler,  reference  to,  40,  114,  195,  237. 

Hay  fever,  Helmholtz  on,  181. 

Eyeballs,  movements  of,  171,  176. 
Eyeball,  muscles  of,  175. 

Heat,  animal,  33. 
Heat,  dynamical  equivalent  of,  49. 

Eye,  changes  in,  in  accommodation, 

Hegel,  reference  to,  20,  268. 

100  ;  reflected  light  from,  73. 

Helmholtz,  Ferdinand,  i 

Helmholtz,   apparatus   for    phase    re- 

FARADAY, reference  to,  91  ;  the  lecture, 

lations,  149  ;   anomalous  dispersion, 

296 


INDEX 


230  ;  as  a  lecturer,  273  ;  as  librarian, 
40  ;  as  a  mathematician,  188  ;  as  a 
teacher,  130  ;  birth  of,  i  ;  brain  of, 
282  ;  certificate  from  rector,  5  ;  choice 
of  medical  profession,  9;  closing 
years,  279  ;  death  of,  282  ;  Director 
of  Physico-Technical  Institute,  185; 
early  days  as  surgeon,  25  ;  early 
friends,  6,  10  ;  ennobled,  279;  essay 
on  energy,  40  ;  first  marriage,  58  ; 
second  marriage,  187  ;  general  sketch 
of  career,  16  ;  gold  medal  in  honour 
of,  280  ;  improvements  on  inductive 
coil,  37  ;  inaugural  thesis,  14  ;  in- 
vestigations on  electricity,  206  ; 
letter  to  Ludwig,  90 ;  on  animal 
heat,  33,  34  ;  on  art,  270;  on  con- 
bination  tones,  160  ;  on  conservation 
of  energy,  39,  53  ;  on  colours,  119, 
124  ;  on  Du  Bois  Reymond's  theory 
of  muscle  current,  108  ;  on  empirical 
philosophy,  256 ;  on  fermentation, 
28  ;  on  hay  fever,  181  ;  on  his  own 
work,  286 ;  on  magnified  movements, 
no;  on  muscular  contraction,  33; 
on  philosophy  of  Kant,  255  ;  on 
physiological  acoustics,  129,  131  ;  on 
principle  of  least  action,  246;  on 
rate  of  nervous  impulse,  59  ;  on  red 
and  blue  and  green,  120  ;  on  relation 
of  physics  to  physiology,  31  ;  on 
superposition  of  spectra,  122 ;  on 
vowel  tones,  163  J  ophthalmoscope, 
71  ;  parentage,  i ;  personal  appear- 
ance, 283  ;  personal  characteristics, 
283,  287  ;  philosophical  position  of, 
250  j  school  days,  3  ;  speech  on  re- 
ceiving medal,  280  ;  speech  when  pre- 
sented with  Von  Graefe  medal,  86  ; 
statue  of,  in  Berlin,  280  ;  student 
life,  8  ;  surgeon  to  the  Red  Hussars, 
25  ;  and  Robert  Mayer,  50. 

Helmholtz,  Robert,  reference  to,  187. 

Herbart,  reference  to,  270. 

Hermann,  Ludwig,  reference  to,  89. 

Hermann,  Ludwig,  on  muscle  current, 
109  ;  on  summation  tones,  160. 

Hering,  reference  to,  13,  119;  colour 
theory  of,  r27. 

Herschel,  Sir  John,  reference  to,  128. 

Heintz,  physicist,  10. 

Hertz,  Heinrich,  reference  to,  190, 
215,  217,  219. 

Hertz,  Heinrich,  Helmholtz  on,  285  ; 
reference  to,  243,  249. 

Hildebrand,  crest  of  Helmholtz  by, 
280. 

Hoffman,  reference  to,  29. 

Horopter,    Helmholtz   on    the,    172 ; 

Horopter,  the,  260. 

Humboldt,  Alexander  von,  reference 
to,  21,  25. 


Hunter,  John,  reference  to,  12. 
Huygens,  reference  to,  114,  239. 
Hydrodynamics,  194. 

ICE,  222. 

Infant,  human,  experience  gained  by, 

258. 
Italy,  King  of,  reference  to,  280. 

JACOBI,  reference  to,  43  ;  on  potential 

energy,  243. 

Jaeger,  Von,  reference  to,  82. 
Jones,  Bence,  reference  to,  91. 
Jones,  Wharton,  reference  to,  77. 
Joule,  on  dynamical  equivalent  of  heat, 

49,  51 ;  reference  to,  91. 

KANT,  philosophy  of,2S3  ;  on  dynamics, 
237  ;  on  nature  of  judgments,  254  ; 
doctrine  of  space,  260  ;  on  the  beauti 
ful,  268. 

Karsten,  Gustav,  physicist,  10. 

Kelvin,  Lord,  on  thermodynamics,  52  ; 
friendship  with  Helmholtz,  92  ;  on 
phase,  150 ;  reference  to,  165  ;  on 
electricity,  211 ;  on  ice,  222  ;  on  dis- 
sipation of  energy,  193  ;  on  theory  of 
constitution  of  matter,  196,  198  ;  on 
Faraday,  206 ;  on  rotational  move- 
ments of  ether,  253. 

Kinetic,  potential,  247. 

Kirchhoff,  reference  to,  10,  43, 107, 184 

Klangfarbe,  143. 

Klerker,  De,  reference  to,  230. 

Knots,  Professor  Tail  on,  200. 

Koenigsberger,  Leo,  reference  to,  236 

Konig,  Arthur,  reference  to,  126. 

Konigsberg,  112. 

Konigsberg,  University  of,  58,  89. 

Kronecker,  Hugo,  reference  to,  90. 

LAGRANGE,  reference  to,  195,  243. 
La  Hire,  reference  to,  78. 
Lamarckian,   principle  of  adaptation. 

256. 

Langenbeck,  Max,  reference  to,  97. 
Laplace,  mathematician,  reference  to, 

Lavoisier,  chemist,  reference  to,  21,  34, 

Lectures  by  Helmholtz,  274. 
Lectures,  Helmholtz  on,  276. 
Leeuwenhoek,  reference  to,  26 
Leibnitz,    reference    to,    40,    44 ;    on 

dynamics,  46,  52,  230,  237,  243,  252, 

287. 

Linnaeus,  reference  to,  19. 
Liebig,  reference  to,  21,  22,  28. 
Light,  theory  of,  114,  116. 
Lissajous,  reference  to,  166. 
Listing,  schematic  eye  of,  102,  178. 
Lobatschewsky,  reference  to,  266. 


297 


INDEX 


Locomotion,    animal,    Helmholtz   on, 

Newton,  reference  to,  19,  44,  52,  44, 

in. 

45,  114,  117,  146  ;  on  the  aether,  199  ; 

Locke,  John,  on  heat,  46  ;  philosophy 

on  action  at  a  distance,  203,  242,  238, 

of,  251,  257. 
Lokman,  fables  of,  3. 

Neumann,  F.  C.,  reference  to,  22,  204, 
207. 

Lotze,  reference  to,  250. 

Neumann,  C.,  reference  to,  205,  214. 

Lovering,  reference  to,  199. 

Nobili,  reference  to,  104. 

Ludwig,     Carl,     reference    to,     n  ; 

letter  from  Helmholtz  to,  90. 
MAGNUS,   Gustav,  physicist,    10,   22  ; 

OHM,  reference  to,  22,  144,  145,  148. 
Ophthalmological  Congress  at  Heidel- 
berg, 84. 

influence  of  teaching  of,  22  ;  death 

Ophthalmometer,  the,  92,  98. 

of,  184  ;  lecture  by  Helmholtz  on,  275. 
Marey,  E.J.,  reference  to,  in. 
Maslceleyne,  reference  to,  70. 

Ophthalmoscope,    invention    of,    71  ; 
theory  of,  80. 
Optic  nerves,  course  of  fibres  in,  174. 

Matteucci,   reference  to,  65  ;  induced 
contraction,  66,  104. 

Optics,  Helmholtz  on  physical,  225. 
Organ  pipes,  Hfclmholtz  on  theory  of, 

Maximilian,  King   of   Bavaria,  refer- 

166. 

ence  to,  149. 
Maxwell,  Clerk,  reference  to,  41,  122, 

PAINTING,  Helmholtz's  ideas  as  to,  271. 

185,  199,  207,  249,  264  ;  on  colour, 

Paionios,  reference  to,  86. 

112,     117;    on    dynamics,    48;    on 
electro-dynamics,   213  ;    on    electro- 

Pallas, reference  to,  74. 
Partial  tones,  147,  148. 

magnetic  waves,  216  ;  on  Faraday, 

Penn,  William,  i. 

205  ;  verse  on  mathematicians,  190. 

Phase,  can  the  ear  perceive,  148. 

Maupertuis,  reference  to,  235. 
Mayer,  Robert,  reference  to,  23,  48, 

Phidias,  reference  to,  85. 
Physical  Society  of  Berlin,  reference 

54,  242. 

to,  41. 

Medal,  ophthalmological,  presented  to 

Physico-Technical  Institute,  185. 

Helmholtz,  84. 

Physiology,  considered  as  a  science, 

Medicine,   lecture    by  Helmholtz   on 

20  ;  methods  of,  29. 

thought  in,  277. 

Piotrowski,  G.  von,  reference  to,  202. 

Mellom,  reference  to,  118. 

Poggendorff,  reference  to,  22,  43,  227. 

Membrana  tympani,  action  of,  133. 
Mendelssohn's    '  Midsummer    Night's 

Pouillet,  reference  to,  60,  62,  64. 
Praxiteles,  reference  to,  86. 

Dream'  music,  134,  284. 
Mery,  reference  to,  78. 

Prevost,  reference  to,  76. 
Principle  of  least  action,  244. 

Meteorology,  Helmholtz  on,  232. 
Microscope,  Helmholtz  on,  232. 
Mirror,  use  of  in  physical  experiment, 

Pseudo-spherical  surfaces,  263. 
Psycho-physical  investigations,  70. 
Purkinje,  images  of,  95. 

no. 

Pythagoras,  reference  to,  148. 

Mitscherlich,  reference  to,  21,  22,  28. 

Mohl,  Anna  von,  reference  to,  187. 

QUINCKE,  physicist,  10. 

Monads,  Leibnitz's  system  of,  253. 
Montgolfier,  on  heat,  47. 

RANKINE,  Macquorne,  reference  to,  91. 

Montpellier,  mathematicians  of,  61. 
Muller,  Johannes,  anatomist,  10,  23  ;  on 

Rayleigh,  Lord,  on  phase,  150,  189. 
Reed  pipes,  167. 

eye,  24,  119,  129,  141,  152,  173,  178, 

Rekoss,  reference  to,  89. 

250,   275;  influence  of,   n  ;  specific 

Reimer,  G.  E.,  reference  to,  41. 

energy  of  nerves,   13  ;    on    rate  of 

Reiss,  reference  to,  43. 

nervous  impulse,  65,  184. 

Rendu,  reference  to,  221. 

Mursinna,  Surgeon-General,  8. 

Resonators,  146. 

Muscle,  current,  105. 

Reute,  on  ophthalmoscope,  78. 

Music,  134. 

Reymond,   Du   Bois,  early  friendship 

Musicians,   indifference   to  investiga- 

with Helmholtz,  10,  24,  35,  43,  60  ; 

tion,  137. 
Myograph,  36. 

on   animal   electricity,   65,  94,   104  ; 
physical  theory  of  as  to  muscle  cur- 

1        rent,  106.  184,  2s?,  284. 

NEEF,  interrupter  of,  37. 
Nerve  cells,  discovery  regarding,  15. 
Nerves,  specific  energy  of,  13. 
Nervous  impulse,  rate  of,  59. 

Riemann,  reference  to,  139,  205,  214  ; 
notions  as  to  space,  264. 
Riess,  reference  to,  22. 
Ritter,  electrical  experiments  of,  20. 

Negative  variation,  107. 

Root,  E.,  reference  to,  210. 

298 


INDEX 


Rowland,  H.  A.,  reference  to,  210. 

Roux,  Le,  reference  to,  229. 

Royal  Institution  of  Great  Britain,  32, 

183. 

Rucker,  reference  to,  207. 
Rudolphi,  reference  to,  76. 
Rumford,  Count,  reference  to,  32,  47. 

SABINE,  General,  reference  to,  91. 

Saccharomycetes,  26. 

Saccule,  138. 

Schelling,  reference  to,  20,  268  ;  on  art 

and  science,  272. 

Schleiden,  botanist,  reference  to,  12. 
Schlemm,  canal  of,  100. 
Schopenhauer,  reference  to,  268. 
Schroeder,  reference  to,  29. 
Schwann,  reference  to,  12  ;  on  fermen- 


Thorax,  Helmholtz  on  movements  of, 

169. 

Tidal  actions,  221. 
Tone,  analysis  of,  104. 
Tones,  combination,  159. 
Tones,  compound  nature  of,  147. 
Tongue  pipes,  161. 
Tyndall,  reference  to,  n,  221,  273. 

UTRICLE,  138. 

VARIATION,  negative,  107. 
Velten,  Olga  von,  58. 
Vibration  microscope,  166. 
Violin,  Helmholtz  on  strings  of,  165. 
Virchow,  early  friend  of  Helmholtz,  10. 
Viscous  fluids,  196. 

Vision,  conditions  of,  92  ;  laws  of,  with 
one  and  with  two  eyes,  173. 


Scotch  Highlands,  reference  to,  92. 
Seebeck,  on  thermo-electricity,  20. 
Seguin,  on  heat,  47. 
Semi-circular  canals,  142. 
Sensations  of  tone,  work  on,  89,  131. 
Sharpey,  physiologist,  reference  to,  14. 
Siemens,  Werner,  electrician,  10,  185, 
1  86. 

Voltaire,  reference  to,  32,  236. 
Vortex  motion,  194. 
Vortex  rings,  197. 
Vortices,  nature  of,  197. 
Vowel  tones,  162. 
Vulpian,  physiologist,  reference  to,  14. 

Smaasen,  reference  to,  107. 
Somerville,  reference  to,  47. 

WAGNER,  reference  to,  134  ;  head  of, 

Sound,  physiological  effect  of,  133. 
Sound  shadows,  166. 
Space,  of  various  dimensions,  262,  265. 
Spencer,  Herbert,  reference  to,  257. 
Spinoza,  reference  to,  252. 

283. 
Waterspouts,  Helmholtz  on,  223. 
Wave  forms,  143. 
Weber,  Wilhelm,  reference  to,  22;  law 
of  electrical  attraction,  204,  207,  214, 

Stahl,  reference  to,  39. 
Steinway,  Messrs,  reference  to,  167. 
Stokes,  Sir  G.  G.,  reference  to,  91, 

Webe'r,  Ernst  &  Heinrich,  23,  153. 
Weber,  C.,  on  electrical  irritation  of 
the  eye,  100. 

195  ;  on  vortex  motion,  197. 
Students,  Helmholtz  on  judgment  of, 

Wheatstone,  reference  to,  91  ;  stereo- 
scope, 178. 

277. 
Summation  tones,  160. 

Wiedemann,  reference  to,  n,  22,  24, 

Sweden,  King  of,  reference  to,  280. 
Sylvester,  Joseph,  reference  to,  190. 
Syren,  polyphonic,  of  Helmholtz,  140. 

William  I.,  Emperor,  reference  to,  279. 
William   II.,   Emperor,  reference  to, 

280. 

TAIT,  reference   to  Prof.  P.   G.,    44, 

YEAST,  studies  in,  27. 

45,  47,  200. 
Talbot,  Fox,  reference  to,  228. 
Teachers,  Helmholtz  on,  276. 

Young,  Thomas,  reference  to,  36,  122, 
123,  124,  152  ;  compared  with  Helm- 
holtz, 287  ;  on  accommodation,  96  ; 

Telephone,  Helmholtz  on  the,  167. 

on  lens,  100  ;  on  light,  114  ;  theory 

Telestereoscope  of  Helmholtz,  180. 
Temperature,  influence  of,  on  fermen- 
"  tation,  28. 

of    colour,    117  ;    use    of    rotating 
cylinder,  62;   Helmholtz,  theory  of 
colour,  125. 

Thomson,  Allen,  reference  to,  14. 

Thomson,  James,  reference  to,  222. 

ZEHENDER,  Von,  reference  to,  84. 

Thomson,  Sir  William,   reference  to, 

Zeller,  Eduard,  reference  to,  267. 

(see  Kelvin,  Lord). 

Zinn,  zonule  of,  101. 

THE    END 


299 


Colston  &>  Coy.  Limited,  Printers,  Edinburgh. 


ERRATA 

Page  233.     Line    4.     For  'on'  read  '  under.' 
„       „  „      5.     Before  '  bodies '  insert  '  heavy.' 

„     237.         „    10.     Insert  comm^after '  Xewton.' 


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HOW  TO   PROLONG   LIFE 

An  Inquiry   into  the  cause  of  'OLD  AGE'   and   'NATURAL   DEATH,'  showing 

the  Diet  and  Agents  best  adapted  for  a  Lengthened  Prolongation 

of  Existence. 

By  CHAS.  W.  De  LACY  EVANS,  M.R.C.S.E. 

This  work  gives  many  useful  and  valuable  hints  for  the  preservation  and 
enjoyment  of  life. 

Price  55.  through  all  Booksellers  and  at  the  Bookstalls,  or  sent  direct  on  receipt 
of  5J-.   T,d.,  Post  Free. 


DATE  DUE 


JAN  31  \( 
MAR 


10797 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 

A     001  068514     7 


